Can you solve the wizard standoff riddle? - Dan Finkel

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You’ve been chosen as a champion to represent your wizarding house in a deadly duel against two rival magic schools. Your opponents are a powerful sorcerer who wields a wand that can turn people into fish, and a powerful enchantress who wields a wand that turns people into statues. Can you choose a wand and devise a strategy that ensures you will win the duel? Dan Finkel shows how.
Lesson by Dan Finkel, animation by Artrake Studio.
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[@TEDEd]

Sign up to be emailed the solution to the bonus riddle: brilliant.org/tededpoisonapples/! Also, the first 833 of you who sign up for a PREMIUM subscription will get 20% off the annual fee. Riddle on, riddlers!

[@rachelletann]

TED-Ed tom riddle

[@dr.sheetaltelge5434]

Hi TED-Ed video was awsm as always

[@nishvaze2666]

We need more quizzes

[@likithvelagala4403]

TED-Ed red Apples

[@katynotperry027]

The odds are the same the chance are 70% to succes

[@fieryskipper226]

I would pick the Noether 5000 because I could just banish myself to the top of a mountain and survive the duel.

[@chrisg2834]

Then you would have eliminated yourself 🤦‍♂️

[@danielyip6797]

That was exactly what I thought as well!

[@danielyip6797]

You may even cast it on yourself again just to teleport somewhere else

[@pressingfile9340]

@@danielyip6797 no cuz its the nearest mountain

[@adamshoneck8590]

My strategy exactly

[@artemisia770]

“There’s still a 3% chance that you’ll all be turned into cats.” I’m okay with that.

[@ronaldjamescastillo1882]

Not until they bathe you.

[@1Peasant]

Becoming a cat turned out to be the winning strategy

[@lupusjoe]

I was wondering why that would be a punishment

[@rhiannontaylor8283]

I would want to be a cat tbh and all my friends know that to😅

[@joemorsi5655]

Solucky, these are my thoughts exactly

[@calumrobertson594]

“Rules stipulate casting with a wand, but say nothing about beating a man to death and then casting.” ~Sun Tzu, probably

[@dominionjay6332]

bestie you are so right

[@pi_man3]

Doesn’t say anything about bringing a gun either.

[@chelseachang8155]

@@pi_man3 *A M E R I C A*

[@hdt8710]

@@chelseachang8155 FR lol.

[@romanscum5678]

​@pi_man3 "bu-but this is a wizard duel! You have to use a wand" "I am. There were just no rules that it had to be magic"

[@hz8nd]

I picked the 60% wand using rules of probability and assuming that the other wizards will attack whoever is the most dangerous existing wizard. My concern with this puzzle is that it is not stated in the rules that you can miss on purpose.

[@londonmason6129]

That’s if they know you missed on purpose also they said you couldn’t ether

[@HappyBuddhaBoyd]

....that is the wrong answer in any case. With the weakest wand, you have the least chance of success. The video's probability is not taking into consideration the assumption that the players will not cast differently than expected.

[@dgendm2736]

@@HappyBuddhaBoyd You are wrong - look at the 3 probabilities of winning on the do not miss on purpose lines - Noether 3000 - 30%, Gaussian 32.3%, Bannekar 38.1%. The right pick is ALWAYS the weakest wand, even without the idea of missing on purpose.

[@cklay1084]

@@dgendm2736 ... How are you calculating that? I simulated the game before knowing you could choose to miss and found the odds were: Noether 3000 - 30%, Gaussian 20.48%, Bannekar 12.75%. This is assuming the other wizards target the strongest living wizard besides themselves, and comparing both targets by the player.

[@lifeunderthestarstv]

thank you! hate riddles that create "rules" you are allowed to break... thats not the point of a riddle xd

[@fabianglathe6131]

There’s just one problem: after those two genius strategists misfire on purpose, the enchantress realizes she’s been setup from the beginning. She looks at your weapon. Instead of the peaceful option that just teleports you, you chose a wand that strangles people to death with vines. Considering her options, enchantress decides that becoming a cat definitely better than death and about 100 times better than becoming a fish, so cat is the best outcome for her, and also misses on purpose. Y‘all are cats now.

[@carloscaro9121]

It says they are in it to make the decision that gives them the greatest chance for success. In other words, they're in it to win.

[@tisajokt7676]

@@carloscaro9121 If these poor wizards have been conditioned to mindlessly prioritize victory in a duel over their condition for the rest of their lives, I feel like they might as well have also been conditioned to not consider the option of misfiring in the first place, wouldn't you say?

[@alisenaqalandar5522]

@@tisajokt7676 severing an arm to save the body is among the most common tactics in the world and would be in the arsenal of any strategist. if the enchantress misses she is absolutely sure to lose, if she casts she has a 10% chance of being useless which is still better than 100%. if she hits, she still has a 40% chance to get another cast. with all that in mind she would never forfeit.

[@tisajokt7676]

@@alisenaqalandar5522 I think your severing-the-arm analogy fits closer with accepting defeat as a cat than misfiring the weapon

[@alisenaqalandar5522]

@@tisajokt7676 severing an arm or misfiring a spell in this case is the equivalent of throwing a battle to win the war. To be turned into a cat would be to lose the war.

[@joncierge7169]

Disappointed that the answer involves “missing on purpose” when that wasn’t offered as a solution. Stabbing the other wizards with a wand would also work, even though it wasn’t listed as an option.

[@Red-vl5bl]

Sounds like Someone missed by accident

[@Ed-1749]

Granted, the 60% wand was correct anyway, even if you dont miss. It's just twice as correct if you can gurantee it.

[@forastero54321]

It was kinda obvious to be perfectly honest (at least for me-someone who is a gamer). You going first makes you the obvious target if you come out strong since the surviving enemy has a pretty good chance to strike you down at the end.

[@mindassassin]

Would stabbing be counted as casting? If not then they wouldn't be allowed to cast until after you do. Then it just turns into a pointy stick fight instead of magic fight.

[@jasonlu9562]

@@mindassassin I cast dual pistols. Now it's a gun fight

[@jarrodvullo5698]

Narrator: "The rules of magic duels are strict" Also Narrator: "So cheese the rules to win the magic duel"

[@Definitely_not_ai]

Loopholes, my friend

[@justin9202]

@@Definitely_not_ai there's a difference between loopholes and breaking rules. Purposefully missing means you are breaking a rule as it never says that is allowed. However as long as a wizard isn't standing after first round your fine, so just sit down, or lay down. You are not standing as per rule subset so it fits in the rules

[@bdogpimpsause]

@@justin9202 we had no way of knowing if you could miss on purpose with a magic wand. Are the wands line of sight, or do you just have to think of your target to hit them? Do the judges know using magic whether or not you intentionally missed? Because if they knew, you would be in violation of the rules and disqualified since you didn’t try to eliminate one of the wizards

[@fehoobar]

@@justin9202 Then you should obviously pick the 100% wand, DISGUISE IT as the 60% wand, miss on purpose and then if everyone is a logical actor and also hasn't BS'd their way here you have 100% chance of winning. Or better yet, BRING BOTH WANDS, this was you have 100% chance of taking out the 90% wizard and 80% chance of taking out the 70% wizard. Adding rules is BS in riddles like this and that only means you can keep on adding more rules and loopholes.

[@justin9202]

@@fehoobar yes

[@ToastyRaviolii]

Take the middle wand, pretend to fire a spell and pretend it doesn't hit, second wizard assumes it's his turn and tries to hit the third wizard because she's most dangerous, she gets turned into a fish and he gets disqualified because he fired out of turn. Bam, solved 😎

[@gametender1]

even if you pretend to fire and pretend it misses that still would of counted as a pass on your turn

[@aegerman6317]

@@gametender1 Why would it count as a pass lol you haven’t casted. The “pass” in the riddle still involves casting. What you should have pointed out is that the video makes it seem like the cast is visible whether it is a miss or a hit

[@randomchipfat937]

Best use of the word" BAM "award Good work

[@amberwerwolfschool8927]

They say that but the second one will also miss on purpouse then the most dangerous one will hit you bc ur more dangerous than the other one

[@zircon8158]

This is the best solution imo

[@plethoras9913]

Me: gets the Noether 9000 and banishes the referee Freeplay mode has been activated

[@markimbing8018]

😂

[@professionalcommentstealer5271]

Well referees aren't really competent at their jobs these days so it'd make little difference

[@littlemiss_sunshine6945]

🤣🤣🤣

[@littlemiss_sunshine6945]

🤣🤣

[@kk_cats6072]

Lmao

[@ricksimon9867]

Well, it has been pointed out a million times, but once more: You did not say that missing on purpose was an option.

[@milliedavis2987]

Hahahaha

[@ryanwilliams9025]

I got it right by thinking of it as hoping I would miss due to the 40% chance to not hit and got the same answer so it didn't really need to be stated

[@lottery7461]

@@JohnSmith-xp9gr He didn't say punching the other wizards wasn't an option either

[@magnusfolke8091]

@@heretic3334 you cant swap wands i would think

[@woogie6785]

@@ryanwilliams9025 actually you would have only had 38.1% since you were banking on it not working rather than intentionally missing

[@cisselah1996]

Obviously, the most humane solution is to find out who my opponents are before the duel, then integrate myself with one of them. I become a friend, a companion, a listening ear and sympathetic shoulder to cry on. Slowly, I start to learn their secrets, their fears, their habits down to the shoesizes. I start to fit into their lives, a steady presence that stays with them even when their other friends betray them and leave (possibly with some help). I touch them softly, speak to them patiently. Slowly, they fall in love. One day, when I'm sure I have them, I ask them out. They agree. I take them to a fancy restaurant, or a movie, or something else I know they like. We start dating. I bring them flowers, presents... I tell them they are the most beautiful thing in the universe to me, the most magical thing I have ever seen. I tell them how my heart skips a beat when I see them, how their embrace comforts me and I feel safe in their arms. How I want to build a life with them. They agree. I start making plans. I buy them a ring. I propose. We have a wedding, a perfect dream wedding, all according to their wishes. Afterwards, we get a mortage and a house. We settle down in a quiet neighbourhood. We wake up i the same bed in the morning, facing each other with smiles. WE eat breakfast and drink coffee sitting at the same table, our hands brusing as we reach for the toast at the same time. When we go to work we say goodbye to a kiss and a 'love you'. Time passes. We start talking about children. We're not sure we want them, but we're thinking about it. After months and months of consideration, we finally agree we want babies, and not long thereafter, we welcome our first child. And our second. And third. Things start to get rough. Changing diapers and working and doing household chores aren't easy, especially with three kids climbing the walls. We start to drift apart. Work keeps us seperate in the days, the kids in the evenings. We have fights. We scream at each other when we think the kids can't hear, and we go to bed facing the walls, a line of pillows between us. I start drinking, they start going out, reconnecting with their friends. They go to bars, to nightclubs. There, they meet someone. Let's call them Robin. Robin is perfect. They're nice and kind and polite, and everything I was but now aren't. They start hanging out. They exchange numbers. It's innocent, just a friendship between two adults, both capable of friendships. One day, Robin kisses them. They suddenly realize what's going on. They tear themselves from Robin, apologizing and explaining they are married, they can't do that. They don't wait for an answer. They take a cab home and sneak inside the house right after midnight. They go straight up to the kids' room, looking at them from the doorframe, letting the guilt of almost ruining our perfect life brew inside of them. A hand lands on their shoulder. It is me. I've been waiting for them to come home, and now I'm looking at them softly and lovingly, almost like the old me used to be. They break down, admitting to their wrongdoing. It's okay though, I forgive them. I tell them I love them. It's fine. We'll get couple therapy. We get couple therapy. The years passes. The kids grow. Suddenly, we are seeing our oldest off to college. Then the second. We start preparing for retirement. A vacation would be nice, we decide, to Greece maybe, or Italy. Maybe Egypt if we decide we wanna see the pyramids. Our third kid starts approaching college age, and soon, they too leave. We are left alone, in a house full of memories, rings on our fingers, grey in our hair. We smile at each other, and we go to sleep in the same bed, facing each other with tender eyes. Then one day, a message arrives for my spouse. It's a reminder for the Duel that is coming up in a few days, and my spouse looks at me with conflicted eyes. They tell me they have something to do, and they'll have to go away for a few days, but they'll be back soon, and then maybe we can go to Mallorca, or Spain? I smile and agree, Three days later, we face each other in the ring. I'm holding the 100% wand, my hands are clammy. I have the first go, so I point my wand at the stranger third party and banish them to a mountiantop. They vanish. Now it's my spouse's turn. They are trembling. They can't believe this is happening. It's just them or me now, and one of us has to go, but they can't bear to hurt me, our children's parent. In a fit of desperation, they turn the wand on themselves, finding this the most merciful solution. The spell misfires. They look up, relief at not dying/being turned into a fish/statue. They smile at me, and I smile back, just as I have every morning for all our years. I point my 100% wand at them, and banish them to a lonely mountain top. Problem solved.

[@matt_kirby]

Beautiful solution.

[@Tomis1101]

I'm crying right now, such a beautiful story with such a sad ending, Shakespeare eat your heart out.

[@caiden2242]

Wow. That was beautiful.

[@Bigzthegreat]

reminds me of the dude that spent months becoming someone's friend just to send them a virus for an extra 50 bucks

[@infiniti2011]

@@Bigzthegreat send link

[@kamelo2219]

Keep in mind how there wasnt a rule stating i couldnt just dodge

[@ManlyKirby]

and there isnt a rule stating i cannot use my revolver

[@silversamurai0267]

Why do I hear Megolovania music coming from your direction?

[@Xadov]

That’s Piccolo talking, there

[@kamelo2219]

@@Xadov DODGE!!!

[@prim16]

Exactly. That's the fault in this riddle. Allow one trick answer, and you allow all of them. Your "dodge" solution is just as valid as the "correct" answer, as such.

[@unclesam7299]

The rules state the winner is the last wizard “standing.” Therefore , standing on a cold mountain after casting the 100% spell on yourself is the most forcing move given the rules of the game.

[@Karajorma]

Or you could just sit down after your go. Sure you lost, but the other guy got fried.

[@fabianglathe6131]

The problem is, they never specified if there are time limits to a round. If you hit yourself with the noether, the other 2 wizards could just wait until you freeze to Death

[@shavedata5436]

Yeah this puzzle is actually a lot less complicated than it is made to be here. If I wrap vines around someone, are they still standing? Can I cast the wand on myself? If so, is my objective to win, or to survive (not stated)? Also, there is no reason to allow missing on purpose as the logic is pretty much the same without the "gotcha" solution.

[@punkwrestle]

Also the beginning says it’s to the death yet none of the wands cast deadly spells.

[@lexikaragiannis3298]

Harvard wants to *know your location*

[@luketownsend5048]

The apples are a 70% survival either way. Unless you miss your mouth on purpose.

[@monticha3274]

Luke Townsend why did this make me laugh so hard lmaoooo

[@liemnguyenhuu7492]

yup that how wizards work lol

[@nitroptics]

Lmao 😂👌

[@rusozawr4969]

Hahahahahahah love it

[@skullcrusherm7425]

Nailed it

[@LaCafedora]

Reminder: this is a deadly duel. To be eliminated, there can be only one wizard left alive. Simply being transported or transmogrified is insufficient to eliminate a player. After the shapeshifting, we must presume that a player walks over to the helpless wizard and beats them to death. Gruesome but logically following given the rules. Therefor I banish Wizard number 2 to a mountaintop. Now wizard number 3 must wait until wizard number 2 either dies or takes his turn. Determining either of these conditions is not going to be easy, seeing as the other wizard is far away, and unobserved by anyone. If they cast before he acts, then they are disqualified, at which point I just need to wait until the missing wizard dies of hypothermia. To take their turn, Wizard 3 must go find Wizard 2. They both die from hypothermia and I win.

[@chalmerskidstv4305]

If someone loses then the next person goes

[@aaronhutchinson8911]

Ok, I guess, but it feels like your reaching.

[@legohexman2858]

You assume that the wizards are limited purely by their choice of wand. Remember these are wizards, not just strategicians with wands. It would not be a stretch to assume that a true practitioner of the mystical natural arts would figure out how to concentrate enough energy, even in the mountain tops, to provide warmth for themselves. An argument against this is that it is against the rules to use any other magic in the duel, but unless they have remote observation powers of the mountain, he could easily buy new clothes and lie about where the wand actually took him, suggesting a malfunction. This of course is not a 100% solution for the teleported wizard but it still does change the numbers.

[@BigHH88]

Wow, you're soo smart 🤓🤓🤓🤓

[@rashminlilamani1744]

Ok.... But how is no one talking about the Hamilton reference Where my Hamilfans at

[@zachzytnick7066]

For the bonus riddle, the odds of surviving the duel are the same regardless of which bowl you pick. Consider the first bowl, where three apples are poisonous, and two are not, and you must eat two. The only way you lose is if you eat two poisonous apples in a row. The odds of that happening are 60%*50%, or 30%. Once you eat one poisonous apple, 2 are left, and 2 are nonpoisonous, hence the 50% chance on the second one. In the second case, where only 2 apples are poisonous, but you have to eat 3 apples, there are 3 ways you can lose: you eat 2 poisonous apples in a row immediately; you eat one poisonous apple, one regular, and then another poisonous apple; or you eat one regular apple and then two nonpoisonous apples. Interestingly, the probability of any individual losing scenario occurring is 10%. Since there are 3 DIFFERENT ways you can lose that are mutually exclusive and happen 10% of the time, you have a 30% chance to lose this way as well. :)

[@clarkalarcon4057]

Thank you so much, I would have never thought of the problem like that😅

[@HelloThere.....]

You are wrong at the end, losing is death, it requires 2 poisonous apples to lose, so 2 normal and 1 poison is okay. Unless it was a typo?

[@freddieban-murray9848]

Thats to much maths for me, i just wrote out the 60 combinations for green and the 20 for red and counted

[@57thorns]

Another way to look at it is to consider the apples not eaten in the case of two poisioned/eat three. You want to avoid two nonpoisoned apples leftover. But there are three nonposioned apples, so if you change the posion status of the apples, you are in the situation that there are three apples you want to avoid, and you have to pick two. This makes the situations exactly the same.

[@BalgaBear]

What I was expecting: logic and strategy. What I got: J.K. Rowling

[@samsunguser3148]

*EXPLIARMUS!* ✨

[@canaDavid1]

@@samsunguser3148 *expelliarmus

[@samsunguser3148]

@@canaDavid1 lol thanks

[@deviantsemicolon618]

Virck and Hamilton

[@imm1nentdeath]

*avada kedavra*

[@sarahtwitt]

This is just like the "What's green and has wheels" "Grass i lied about the wheels" It has an aspect that isn't specified

[@aaronnavidad539]

Thats from perrys secret joke book right

[@leothesquid4099]

No because they never said you couldn't miss. Your example explicity states it has wheels, completely different

[@woosh5102]

Right, this example is lying about a rule. The other is not mentioning a rule but still not denying it

[@evetheeevee2977]

A green car

[@samlee5549]

I remember a movie with a quote which this reminds me of. Puzzler: What has 4 legs at morning, two legs at noon, and three legs at night? Protagonist: Simple, Man. Now, answer my riddle. What's green, can fly, and is nailed to a wall? Puzzler: Uh, I don't know. Protagonist. Then Let me pass. Later, when Protagonist is exiting. Puzzler: Wait, what was the answer? Protagonist: A Red Herring! You can paint it green, put it on an aeroplane, and nail it to a wall with a nail!

[@wezajamison-neto1905]

The problem about this is we're assuming the adversaries have the information on all your wands. The narrator never specifically said the other wizard had all the info on your end and they're probabilities. Realistically, this wouldn't work out because even if you know your opponents strengths and abilities, that's not to at they know yours. If they didn't know your wands probabilities they wouldn't bend done this most likely, but I understand the concept.

[@necro-claud6370]

It's game theory

[@Santaxe]

Consider these two direct quotes: 1.) "You are chosen to cast the first spell, the Newt-niz magician will go second, and the Leib-ton enchantress third" 2.) "Anyone who casts out of order immediately forfeits the duel" - if you go first, using your 100% accuracy wand to eliminate the Newt-niz magician. Then, the only remaining wizard, the Leib-ton enchantress, will go second (though she is expected to go third) and she will immediately forfeit the duel for casting out of order. You win.

[@meltinor7917]

This might be better than the “correct” answer

[@MCart1215]

Lmfao dude this is actually genius hahaha

[@olaf-chan-728]

they are banished to a moutain, the Newt-niz knows the rules and will wait until the enchantress comes back

[@TheYouOzi]

With these strict rules, there's no way Griffindor can win. Dumbledore: However...

[@AngelA-ym2jz]

*Gryffindor

[@keanureeveslusciousweave]

HAHA YES I WAS WONDERING WHEN I WOULD STUMBLE UPON A HARRY POTTER PUN IN THIS COMMENT SECTION 😂😂

[@amazingango9103]

@Anish Golikere It sounds rather like the Triwizard Tournament

[@prinshiahirwar5698]

Dumbledore : *"1000000 points to Harry Potter!"*

[@MagyarGaben]

Dumbledore: I'm about to do what's called a pro gamer move

[@solar_panei7086]

“You have been chosen as a champion” *and that, my friends, is where it all went wrong*

[@jnull7655]

(me dies of heart attak)

[@ToeJoe123]

Gaussian and you miss on purpose be like:

[@cozyflurry]

Mhm

[@cozyflurry]

@@ToeJoe123 ;-; yep

[@BeetleDragon]

Alternatively: I really hate duels so I choose the teleportation wand (while secretly also taking the vine wand) and just teleport myself to a mountain and use the vine wand to get down by shooting vines at things, that way I live and have a 0% chance of being something other than a person.

[@UltimaDoombotMK1]

Plot twist, the mountain is so cold that you freeze to death immediately, giving you a 100% chance of becoming an ice sculpture. Oh well, looks like you lost

[@gama5942]

I have a foolproof method: dash behind the enchantress, hold her up to be turned into a fish, throw the fish at the other wizard to discombobulate him, then spam my m1 until my chance works; what if the genius strategists already predicted their opponents' next moves? They're geniuses, after all.

[@lifedeather]

discombobulate

[@Fluffers355]

This comment doesn’t get enough attention

[@SoraRaida]

Discombobulate

[@danielgehring7437]

Run. Use deadly, never-miss wand on police. Begin lifelong career in magical crime.

[@BlazeTaleo]

Daniel Gehring but they don’t even die, they could get back and eventually you’d be overrun

[@scroonkgun-7875]

How tf they gonna get back from like 100000000000000 miles high mountains

[@somespacepizza1757]

They'd probably have a magic barrier, which is why you can miss a shot without being disqualified for endangering the audience...

[@TheAllMightyGodofCod]

Better yet, use the 100% accurate Noether on yourself and then climb down the mountain. Oh, don't forget to take your best coat or fire wand to the tournment-

[@net_lag]

No miku. ! Just no

[@doddermodd]

"You'll all be turned into cats" is a very questionable choice for a punishment

[@ugneiljinaite4369]

Actually I would like to be turned into a cat

[@main3240]

@@ugneiljinaite4369 Furry

[@jodyceslok1913]

@Andrew Ford I agree too. Any other way, you'd die. If you were a fish, you'd suffocate. Turned to stone, all of your organs would also be turned to stone, meaning you'd die. I wouldn't even mind being a cat, since you'd still retain your original knowledge. If i was the enchantress and everyone else skipped, it would actually be the logical thing to do, or else you would be targeted by lethal spells. Also, cats get to sleep a lot, be cuddly, and not really have to do work. Why? Because they're cats.

[@kaylakaty132]

I WANT TO BE A CAT

[@Halleretta]

@@jodyceslok1913 Turning into a cat woulds seriously hurt you... Cat's bone structures,Organ sizes,Muscle tissues etc...Are all diffrent to us so turning into a cat could seriously injure our Physcial body and Maybe kill us

[@17thstellation]

There are a couple of problems with this one, honestly. As others are pointing out, it was never stated that you could miss on purpose, and it really feels more like the kind of answer you'd hear as a joke. Also, it wasn't clear that your opponents being perfectly rational just meant they'd target the person with the most powerful wand. I kept on thinking about how they'd just get stuck trying to predict and out-metagame each other, and it quickly became obvious that this scenario doesn't allow for any line of thinking to be consistently optimal.

[@DWN037]

Not to mention that it's not a perfect strategy anyway - there's _still_ a 3% chance it ends in a draw, and a 60% chance to win at the second round isn't as sure-fire as it sounds.

[@kriojn]

Considering the thing is 3 players and would pretty well end before a third round, the decisions that can be made by any one player is miss or target the most powerful player. Like sure you try mind games by idk pointing the wand at yourself, missing purposefully (presuming you can hide that it was on purpose), playing it off that you are sad that it missed and having the others not target you- but like imagine if that was the solution to this probably riddle… the comments would be even more enraged

[@timm8998]

They do what gives them the best odds of winning, that is the rational thought. I think it was pretty obvious. It is not a problem with the riddle, this is how they work.

[@lenoncerqueira8308]

I actually wrote down a rigorous mathematical solution for a version of this problem in which you cannot miss on purpose. In short, it can be demonstrated that, for your opponents, targeting the person with the most powerful wand is, indeed, optimal (in that it maximizes their probabilities of ultimately winning) in all cases. And the final answer is, still, that you should pick the 60% wand (and target the third wizard in your first move). You're thinking the game gets really complicated down the line, but it really doesn't. The reason it stays simple is that, within one round, either someone wins, or everyone loses, or the duel becomes a one versus one, which is determined by pure chance since the two remaining wizards make no further choices (they only have one opponent to target, and remember, they can't miss on purpose). Therefore, any "strategy" they could come up with goes no further than one round. I was also frustrated by that "miss on purpose" solution (especially after I spent some time solving a different riddle). I'm sure I could adapt my solution to this possibility, making it rigorous, but I don't think it is worthy of such treatment.

[@MasterlyRex8789]

No missing on purpose is how you are supposed to “think outside the box”. This is supposed to be a riddle. Not a math question. The real issue with this riddle is not eliminating the infinite nonsense answers.

[@EbonMagician34]

Banishing yourself with the 100% accurate wand is part of a potential alternate solution. With yourself gone, the other two wizards can only eliminate one of the two of them. This would result in a draw, except that since your wand is 100% accurate, you can banish the remaining wizard, even from great range, to another mountaintop. After this, you can (in theory), return yourself by reversing the spell, while they are incapable of doing so: leaving you as the only remaining wizard on the match grounds.

[@sharlo3799]

theres another problem, you’d be stuck on a mountain in the middle of nowhere

[@BigHH88]

You'd be eliminated

[@SomeGuy-lr7ms]

Host: alright no missing on purpose Me: YEARS OF ACADEMY TRAINING WASTED

[@theprocess2357]

Some Guy you still have the best chances of winning with 60% wand even if there is no missing on purpose

[@shavedata5436]

It's the same even if you can't miss.

[@fireblaster8916]

Then I barely miss so everyone thinks I have bad aim

[@luxurious0346]

The best way to win is to miss on purpose *_wait, that's illegal_*

[@pirmund9191]

damn, 1k likes but not a single comment.

[@polyspheremusic3417]

Second!

[@FedorFan101]

dont know why i laughed so hard

[@pauinesaldana9178]

@khurshed Ul Haq. khan lol

[@Nylspider]

Exactly I was like, you aren't allowed to bent the rules like that

[@sorenlily2280]

The thing is, even if missing on purpose were not an option, the logic is almost exactly the same, and the optimal strategy would still be to pick the Bannekar and then target the enchantress. You still gain a huge advantage if you miss on your first round while also being the weakest target. This is because if you miss, neither the sorcerer nor the enchantress will target you on their turn because you're weak, so if either of them hit, you always get to go first in the ensuing 1v1. However, it does become more of a mathematical exercise than a logical one to prove that the Bannekar is actually the best. The percentages are tight so you can't do a quick estimate. But if you work it out, the Noether 9000 (100% wand) gives a 30% chance of winning, the Gaussian gives a 32.34% chance of winning, and the Bannekar gives a 38.11% chance of winning. This is actually a really interesting math problem if you ban missing on purpose and start generalizing to different percentages and more people. The problem gets really complicated really fast with more people because it has recursive properties. Not a good logic puzzle though.

[@theeraphatsunthornwit6266]

Since you seem to be quite good at this. Let me ask you something. in the video, how come choosing noether 9000 and miss on purpose has 1.6% chance of winning... if you pass, orange will pass too, then yellow will try to kill you, if she succeed you die, if she fail, everyone turn into cat... which you 100% lose anyway.

[@Muhahahahaz]

Actually, no. The problem with their solution is that you now have a 64.6% chance of winning. This means both wizards will actually target you, because they are “Masters of Strategy” and can therefore calculate your optimal strategy (Of course, this ultimately lowers your odds, and makes the puzzle a lot more complicated… With everyone reacting to each other’s optimal strategy until an equilibrium is reached. Which is why missing on purpose is such nonsense, unless they’re ready to introduce game theory in a 5 minute video lol)

[@sorenlily2280]

@@Muhahahahaz I'm not sure what you're talking about. The players want to maximize their own chances of winning not minimize your chances of winning, so your chance of winning is irrelevant to their strategy. If your opponents start colluding, then the equation might change, but we're not considering collusion. So, the video does in fact describe the optimal strategy for each player. If you think it doesn't, then please explain how any player could do better than what is described.

[@KaRma20.10]

How you calculated that chance of winning is 64,6%?

[@zephalverilion5393]

I like how they tell you that you can miss on purpose after you are supposed to answer

[@21Kikoshi]

lol yeah that needed to be in the rules, but thats how they make is difficult to solve if they dnt tell you all the rules

[@michaelthomas8077]

The toughest riddles around! The ones that leave out information!

[@CSmyth-]

What information is missing?

[@jepperspeppers5900]

It doesn’t explicitly say you can miss on purpose

[@jj3665]

While, yes, it is marginally annoying that they didn't explicitly provide you with the option to intentionally miss, you can still arrive at the correct answer without that information. Check out the odds of winning at the end; your best chance still lies with the 60% wand (at around 38%).

[@yunogasai5416]

@@CSmyth- kzbin.info/www/bejne/ZpmmoYOiebJjiLM

[@worm489]

@@jj3665 have to side with the op on this.. if you want to pose the surprise info that missing a shot is valid, then you must also concede that the vine spell doesnt incapacitate your target that remains standing, alive and not transformed. Congratulations, you will either lose to probability, or lose to being a cat as your opponent will never be "not standing"

[@fortello7219]

I didn't realize you could choose to miss, but my answer was the 60% and "hope" you miss. After all, going first in this is pretty much the worst position.

[@sevenbrokenbricks]

Fortello that was my answer too, maybe it’s all the d&d but the idea of being able to intentionally miss with the spells presented makes little sense.

[@AkshayAradhya]

Same. Very bad problem statement

[@edgycunt6358]

The riddle stated that we take turns casting spells and that after 1 round the game is over. So the riddle is flawed since a spell is casted wether it lands on an oponent or not.

[@Lagspike99]

same here

[@perfectlyimperfect423]

Fortello Same. I wanted to target the 90% and hope that it doesn't work.

[@TJBrumfield]

I assumed the best strategy would be to use the banishing rod on yourself. While you may not win in the traditional sense, you have a 100% chance of getting yourself to safety and surviving. Isn't that better than a 60% chance of surviving?

[@TheNeilBlack]

Your goal isn't just survival, it's to win the duel. Banishing yourself to a mountain is therefore a failure.

[@joshhicks4591]

I agree with your answer and it's as logical as "oh, I'll just miss on purpose." This riddle is just: pick the answer that we already thought of and you win.

[@BigHH88]

Safety? A distant mountain top is safety??

[@mechavos4066]

More like: 100% chance of freezing to death

[@tortenschachtel9498]

@@mechavos4066 For the unprepared, maybe, but you are supposedly a wizard.

[@alexgac1801]

Here is the solution for the basket of apples : take the red one then miss your mouth on purpose on one or two of the bites. And voilà, you didn't eat two full apples so you won't die !

[@WillRennar]

Arrive at the duel with cold weather gear and provisions. Take the 100% wand, use it on yourself to poof right out of that mess. Climb down mountain or become mountain hermit at your discretion. "Not a statue or fish" is win enough for me, thanks.

[@pinnacleexpress420]

This is lowkey the best answer and needs more upvotes.

[@Espartanica]

That’s what I was gonna say!

[@cerulean22b69]

this is the real answer! lol!

[@HypaSnypa12]

I literally thought that this was actually the answer because at the end of the round everyone in the circle would've been turned to cats and you'd be in the mountain safe. The people at Ted obviously don't play D&D. LOL

[@legionofelites2547]

You could also call in a plane before so your prepared for the cold and have a flight home

[@redzoro92]

The answer to this is just dodge the other wizard’s attack.

[@croassung3721]

...

[@GanoFin]

Doge

[@zeycus]

Yeah, I think that is a flaw in the solution. Even if you are not allowed to miss on purpose, the best wand is still the 60%. And you still realize you would be lucky if you miss the first spell. So the problem is still beautiful and has a beautiful solution, just not the one proposed in the video.

[@xxMilakasiaxx]

@@zeycus are you sure? what is the probability to win with the 60% wand without missing on purpose? cant figure it out myself.

[@jackgooding5808]

xxMilakasiaxx 38.1%. The table of solutions is at 4:07

[@thomastismyname9203]

I came up with the correct answer without thinking that you could intentionally miss. Because my thinking was that you wanted the strongest possibility to miss your first shot (but also large enough to hit the next) so that you aren't the next target. And then with the weakest wand you would be the least likely to be targetted after you miss. Neat!

[@IIswagdelicious]

Oh. Wow I was off. I picked the tree wand on the basis that the other two might actually be useless. Just because someone is bound up my vines doesn't mean they can't cast a spell, and nothing says that spells are limited by range, making the wand that sends someone to a distant mountaintop useless as long as they know your location, which they would, since they were just there. The only wand that actually guarantees the person struck by its spell cannot cast THEIR spell (granted the spell works) is the one that turns them into a tree. Can't cast a spell if you can't move, hold your wand and have no brain.

[@Luffy-su1ho]

My thought process was that I could send myself to the mountain top (since using a spell on yourself is not prohibited by the rules) and since I'm technically standing at the mountain top, I can simply wait out the other two. Alternatively, I could send myself back and push the remaining wizard onto his back (physical force to make him "not stand" is also not prohibited)

[@michaelryan69]

Rules say that you only have to be left standing. If you get turned into a statue, are you not standing forever, outliving the surviving wizard and thus winning the contest?

[@e5858]

As long as it’s a standing statue, and that would be the same for everything else but the fish

[@VioletNKisHere]

Perhaps they meant standing alive.

[@bardock2525]

"I've won. But at what cost?"

[@Aostrele]

@@VioletNKisHere r/youknowwhatimnotgonnasayrslashwooooshbcuzimnice

[@janesharp2895]

@@VioletNKisHere r/woooosh

[@THUND3RCOW]

Take the 100% wand and use it on the judge/referee. NO RULES. WIZARD ANARCHY

[@damiennewman1992]

And then you're seen as the biggest threat and are simultaneously attacked by both the 90% and 70% wands. Even if you respond quicker than they can interpret what happened (since it would be a surprise), you are only going to be able to take out one of them before the other responds. Best case scenario you have a 70% chance to lose assuming you take out the wizard with the 90% wand.

[@limilach3214]

@@damiennewman1992 still a 30% chance of survival, I'll take it.

[@damiennewman1992]

@@limilach3214 The suggestion in the video is above 50% chance of surviving and you'll go with the 30% chance?

[@reeree6048]

@@limilach3214 its like a 5 percent chance because they are both higher then 50 % almost 100 % chance of death

[@limilach3214]

@@reeree6048 still I'll take it.

[@LeTtRrZ]

The real strat is to choose the 100% wand and tell your opponents you will cast at the one who does not forfeit first. Each of the other opponents will get scared that they will be the target if the other immediately forfeits, so each will immediately forfeit. If neither forfeits, lay down, take a nap, and settle in for the long haul.

[@emberdragon3436]

I thought that if you used the 100% Noether 5000 on the second wizard, then they’d technically still have to do their turn, because turn order has to stay in order. So the enchantress couldn’t go until he does, and he can’t go, so technically you win

[@aegerman6317]

The detail of what the wands do doesn’t matter at all. Banishing them to the mountain top is eliminating them all the same as turning them into a tree

[@PostKillSandwich]

Take the 100% chance wand, cast on red wizard. Since red wizard's gone, yellow is up next. Since yellow was supposed to go 3rd but now is forced to go 2nd, she must cast out of order, disqualifying her. Boom, you win.

[@maxentirunos]

Another possibility if the others don't know your success rate and spell effect. Take the 100% wand, miss the first shot, second WILL take on the greater threat (being turn stone 90%) and try casting at him. He did it good, then it's your turn to blast him on a mountain, he failed, the other WILL retaliate and may turn him to stone. he did? Blast him on a mountain. Neither did it? repeat the turn. If the first condition isn't respected, then your solution is good.

[@foomples]

But that wasn't in the rules. She wouldn't be going out of order, this would pertain to "skipping a turn" whether it be willing or not.

[@AI-hl5xl]

i agree with maxentirunos, if others don't know your success rate and spell effect, the other will try to eliminate the greatest threat for them, in this case, 70% will try to eliminate 90% and vice versa, if they know ours, eliminate the 90% first for me, the rest is up to rng god

[@CalliePossum]

Pray to RNGsus.

[@shahsadsaadu5817]

PiepowderYamen Dango that is what I thought

[@sharkbrother6596]

I pull out a glock and perform the most powerful spell of all.

[@tdestro9_362]

Your neutral B

[@donttrustnoone3921]

Avada Kegunshot

[@seraphim9219]

@@tdestro9_362 most underrated comment i have ever seen

[@elijahkauffman]

Death

[@williamg7123]

America has entered the chat

[@robertmallette-lx1lc]

I think the fact you can ‘miss or don’t miss’ is a direct contradiction to the fact the wands work on a probability system & literally means varying levels of randomness that therefore cannot be controlled in this way.

[@godther1391]

regardless your chances are highest with the 60% wand, even if you have no choice if it hits or not

[@ice2163]

This is literally me back when I played basketball during my high school gym class. The gym teacher would have the entire class warm up by shooting and passing wi5 each other and during that time she would be watching as to who was really good at the sport and those who are not. When the games begin she would balance the teams with good and bad players. Having experienced the exact same thing in my grade school I purposefully missed shots and acted like a student who doesn’t care about the sport. The strategy worked. The gym teacher later paired me up with two other student who are in the high school basketball team. We basically crushed the other teams on 3v3. I had my fair share of getting the ball at the corner of the court and doing a Kobe spin shot for a 3 pointer. This video reminded me of that memory.

[@worker-wf2em]

So the solution relies on a condition that wasn’t stated in the setup, namely that you can miss on purpose. In the spirit of this absurdity, I propose a better solution is for all three wizards to sit down and deliberately miss, and given none are left standing then none would be turned into cats and everyone survives.

[@Grivian]

Genius

[@MiiNiPaa]

Main problem is that this video takes classc Martin Gardner's "Three way duel" problem and replaces guns and no-perfect-gunslingers (where common sense dictates that you can miss and miss on purpose is extremely hard to discern from honest miss) with magic and wands which just sometimes doesn't work (where common sense does not work, because magic)

[@mikeluit3027]

I was just thinking the same thing before unpausing the video. The best strategy (to quote "Wargames") "is not to play".

[@xwingknight]

Now you’re thinking with portals!

[@derekhandson351]

but if all 3 miss, they're all still standing

[@cjortiz]

After your masterful strategy to 'miss 1st', the Newt-Niz sorcerer (also with mastery of strategy) also misses on purpose to maximize his chance of success. The Lieb-Ton enchantress (also with mastery of strategy) recognizes and accepts her position in this prisoner's trilemma, and condemns everyone to the Nash Equilibrium by also intentionally missing her shot.

[@colmecolwag]

But the Entrantess would still have a Greater Than Zero chance of winning if she zapped the sorcerer and tried to luck out against your wood wand, giving her a 37%ish chance to win compared to her going "how about we all lose" which has a 0% chance of winning

[@ideecay2190]

@@colmecolwag Thats the joke I think.

[@mostafaabdelmalik8434]

@@colmecolwag a guaranteed draw for me is better than going 40% versus 60% in the blue wizard's advantage, I would miss on purpose too

[@colmecolwag]

@@mostafaabdelmalik8434 i mean its not a guaranteed draw, its an Everybody Loses. Its not even "If i dont win, nobody wins" since you still got decent odds, even if theyre stacked against you. Its just throwing the duel out of spite.

[@mostafaabdelmalik8434]

@@colmecolwag true

[@Posiadam.]

Well, if missing on purpose is the “correct” option then from the 1st player perspective the best way of winning is just to sit down and wait for the natural death. You have 100% of winning that way, because nobody else would have a chance to cast any spell before you and the round is still going, so the judge can’t do anything.

[@quesin5162]

I’m proud of him for involving Hamilton and ,”Not throwing away that shot,”

[@CptCelestialCarnage]

My logic was to take the 100% staff to send the 70% dude to the mountain, thus being unable to cast. This should however automatically disqualify the 90% lady since she woud be casting out of order. That was in the rules.

[@TopOfLobby]

Kaupo This could work however the banished wizard could still go leaving it to be the other wizards turn. Now what’s the probability that he does go.... yeah I don’t care enough lol

[@AnonYmous-mc5zx]

@Jason Achilles That makes it an even more valid plan to cast the banish spell on yourself. "Welp I guess I'm no longer part of the duel, now to just use my EXPANSIVE KNOWLEDGE OF MAGIC to get off this mountain."

[@medexamtoolsdotcom]

How about this plan. Bring a machine gun to the fight and shoot them all.

[@dannyt7456]

But the wizard would be removed therefore she wouldn't be casting oit of order

[@subbaiahkasi6310]

medexamtoolsdotcom Yes and then get turned in a chicken by the judges, while they heal themselves...

[@maggielu3927]

“you’ll all be turned into cats” *bold for you to assume i don’t want that*

[@omori3703]

*bold of you to assume I’m not a cat*

[@Milkcake00]

I am a cat

[@strawberryseal1851]

*Warriors (Warrior Cats) intensifies*

[@Milkcake00]

A cat

[@Milkcake00]

I AM A CAT!!!!!!!

[@justapt01]

Second round Banneker: *ACCIDENTALLY* misses Me: *guess I’ll die*

[@Kazutoification]

Another way to think about this riddle... Imagine you're in a three-way stand-off with rudimentary fire-arms. Your fire-arm has a 60% success rate of firing and hitting your target (that can be due to the weapon itself or your lack of training with the fire-arm), while the two others have 70% and 90%. In this situation, there is no turn order that must strictly be followed and no peaceful solution exists. If you fire your fire-arm, you won't have much time to reload before you are fired upon, so you realistically have one shot. The best possible solution would be that you take the initiative and misfire. Assuming the 70% and the 90% are judging the situation to maximize their success, they will ignore you. Instead, they will fire upon each other because not only are you a non-threat, the other person's threat level is exacerbated. They shoot each other, and you have a 70% chance they pick each other off (maybe 63%). You then have a 30% chance of having to face against the 90% person, but since you've taken the initiative, you can simply reload quicker and finish them off.

[@zackwalker1789]

In this situation without turns existing there would be no point in misfiring as you could just wait for the others to fire at each other and then fire if there's one remaining afterwards

[@Candlelighter]

Take the 100%. Cast it on yourself. Youre still standing, just on a mountain

[@wenceslay543]

Exactly what i thought lol

[@Sybaification]

I thought the same thing. Lol

[@2010RSHACKS]

Forfeiture doesn’t win the game

[@RamdomView]

Then the rest of your wizarding club beats you up for shaming them in front of public eyes.

[@thetinykid4169]

@@2010RSHACKS he doesnt forfeit. It was a battle to the death. He is still alive.

[@kekohokko7213]

Call me pedantic, but I read "take turns casting spells to eliminate each other" as a stipulation to always aim at a contestant. With that in mind, I would have taken the 60% wand, aimed at the enchantress and hoped for a misfire.

[@kangar1797]

oh my god THANK YOU i though i was crazy

[@kampfkanguru1951]

@k I personally think after making the math that the 60% wand is the best choice and it's chance to win is certainly higher than 24%. In 60% of the times you eliminate one wizard and have a 30% chance to win. In 40% of the time you miss, and then it's important what happens next. In 3% of that 40% both wizards miss and everyone loses. In the remaining 97% of the 40% one of them is eliminated and you have a 60% chance of eliminating the other one. So your chance of winning with this strategy is about 40%, not 24%. If I made a mistake there, please let me know. Edit: I just watched the end and they showed the odds of winning without missing on purpose, it's 38%.

[@PlatformingCyndaquil]

Gets hit by spell…Hey Luz.😭

[@Haunted2077]

If it did hit, and work, they would still be in the contest, or duel. The riddle says "whoever is left standing will win." The first and third wand would definitely leave those that it hits still standing.

[@PlatformingCyndaquil]

@@Haunted2077 I think they mean standing and able to do something while still in the circle, so no.

[@RafaelMunizYT]

step 1: choose the best wand step 2: cast a spell on the witch step 3: before the wizard casts his spell on you, confirm he has green eyes step 4: he's asked to leave the tournament

[@77madman]

As I'm watching the video, this is my idea: Use the 100% wand on the 2nd Wizard. If he is bound then the 3rd Wizard must cast, but would be disqualified because she's casting out of turn and the rules did not offer that detail saying that a wizard turn is skipped if they are unable to cast.

[@perfumefemur]

Good point

[@markfrye5358]

That’s exactly what I was thinking all along! 100% chance of winning.

[@thecodwa8427]

the true genius

[@KronusToketsu]

except the 100% wand doesnt bind, it banishes. the 60% wand binds

[@QuokkaWaka]

@@KronusToketsu True, so he'll just fire wildly and the 3rd wizard won't be casting out of turn

[@marcvanleeuwen5986]

With 3 participants, it is not a duel.

[@collinbeal]

Marc van Leeuwen It's a trial B)

[@brucetucker4847]

There are two kinds of people in this world, my friend... those who know how to win a 3-way duel, and those who dig. You dig.

[@mackharris5356]

You my friend solved the true riddle

[@OneNidim]

Marc van Leeuwen it’s a duel not a Dual

[@madhavsingh1661]

Marc van Leeuwen Only two at a time sirr.. Thatswhy it's a duel

[@brookepearson]

Before I heard the answer, I went with the Gaussian. My thought was that, because the rules are so strict, it was going to take the rule about no one being left standing _literally_ and they cannot be physically standing at the end of the round. The wand with the vines (Bannekar) would still leave your opponent upright and on their feet, just wrapped in plants. The teleportation wand (Noether 9000) would leave your opponent in the same position (standing), just in a different place. The tree wand (Gaussian) would turn your opponent into a tree, so it would be a tree standing there, not the wizard.

[@ilove2eatnsleep]

The table at the end can't be accurate. For instance, if you take the Noether, and miss on purpose, you should have 0% chance of winning instead of 1.6%.. Turn 1: You miss on purpose Turn 2: Wizard #2 has 3 options. 2a: Miss on Purpose 2b: Attack You 2c: Attack Wizard #3 2a Gives W#2 > 64% chance to Win 2b Gives W#2 < 37% chance to Win 2c Gives W#2 < 30% chance to Win So they choose 2a. Turn 3: Wizard #3 has 3 options. 3a: Miss on Purpose 3b: Attack You 3c: Attack Wizard #2 3a Gives W#3 0% chance to Win 3b Gives W#3 < 36% to Win 3c Gives W#3 0% chance to Win So they choose 3b. This means they have 90% to knock you out, or 10% to turn you all into cats. 100% You Lose. The only way to win is to knock someone out in the first round, or have one of the other wizards knock the other out. With a 100% successful wand in your hand, you are a MUST target, so they will never target each other. So that 1.6% is incorrect.

[@aon02b]

Unless one of the others accidentally fires out of turn and eliminates themselves. But then that would also mean the other 0% option shouldn't be 0%

[@zacharyrotunno6859]

Step 1: Confirm you have green eyes Step 2: Ask to leave the duel

[@Kizaco]

Knew I would see a joke about this

[@lovelyrookie3368]

@@Kizaco Same. I was searching this type of comment and here it is. This kind of green eyes jokes are on every video.

[@VioletNKisHere]

Yep on every Ted Ed riddle video

[@christophervandehey2614]

3. STOP USING THIS JOKE

[@VioletNKisHere]

Step 1: make a joke about another riddle Step 2: there is no step 2

[@missm8067]

“You’ll all be turned into cats.” Did Professor McGonagall make that rule?

[@keanureeveslusciousweave]

HAHA MOST LIKELY 😂😂

[@carissanieves6452]

XD 🤣🤣😂😂😂

[@jyotisrivastava1122]

100% It's Professor McGonagall

[@GDPlainA]

Also McGonagall: transfiguration to students is illegal as a punishment

[@kalaivanikumar7493]

Ha finally, found some fellow potterheads

[@hola-5897]

Okay but the wand has a 60 percent chance for the spell to work. There's still a 40 percent chance that the spell won't work and that's barely below a 50 percent chance which is half and half. So at the beginning of the second round, there is still a good chance that the spell won't work on the other wizard and he will probably turn you into a fish. In the other scenario it's the same thing but the enchantress can turn you into stone.

[@lifedeather]

true just give me the 100% accuracy lmao

[@christopherfloody5555]

Pick the least reliable wand, shoot to sky, meaning you are the least threatening of the two targets. This means that the second wizard would be best served targetting the third wizard. If he hits, its your turn to target him. If he misses, then wizars three is best off still targetting him, as she is most threatend by his accuracy over yours.

[@peterskrobola8753]

Wait, you never said the other wizards would know how powerful my wand was.

[@itzdjyar]

@@omikumo Still, when you have a giant convoluted set of rules, and then still manage to leave out things or leave things to assumptions, maybe it was too convoluted to start with?

[@lydiasteinebendiksen4269]

If they didn't know, they couldn't really act as perfectly rational agents, making who they target almost random, and at that point it's more a guess than a puzzle.

[@exotemp5949]

@@itzdjyar I agree, when did anyone say you can purposely miss, at that point, if the spells can be purposely missed, why not just say, "I'll just use noether 9000, then dodge the 70% wizard spell and win next turn". Also I don't see how it's possible to use Noether 9000, purposely miss, then win 1.6% of the time. The 70% wizard will miss on purpose, so that the 90% wizard has to attack you in order to not be turned into a cat, and have a 30% chance of winning if she hits you, and if she misses, you are all cats, so it should be 0% right?

[@drhoneybadger]

Yeah, really fucks the logic

[@331mty]

Was there anything about missing on purpose

[@Mohit-jl8kl]

The master strategy is Don't participate in such a dangerous game

[@chesthoIe]

But what if it's the only game in town?

Take the 60% wand. Miss on purpose. Cast out of turn after the second wizard tried, get disqualified, survive. Take the 100% wand. Find the one who made the rules. Blast them.

[@izzy-artmusicvlogs1234]

Sean -Chesthole- Osman You still don’t have to play it.

[@ouch9841]

You Wouldn't Gain Fame Then.

[@rebeccavecchio4275]

I agree lol

[@firstnamelastname9237]

Riddles are prone to an excess of options. (Or wrong solutions) For instance, sitting down to not be a cat. Running behind another wizard to avoid getting hit. The usage of the word “target” can imply that rules 3 and 4 completely remove the possibility of missing on purpose (only on accident), and make number 2 impossible as everyone in the ring is actively a target until they are eliminated. While eliminated from the duel, it doesn’t say that you don’t count towards the standing count, meaning the only way to be sure you don’t become a cat is to not stand or if someone becomes a fish. Meaning unless someone doesn’t stand, there’s at least a 30% chance regardless that you still become a cat. Edit: if target ONLY applies to the spells. You could potentially just manhandle or attack someone suddenly and have the other one hit with a spell and make sure they’re not countable as standing. You don’t have to eliminate the person you beat, just make sure they aren’t standing. As it goes till one is standing.

[@Alexandr.A.P.]

Actually a good lesson - appear weak, especially when you're not, and strategize the outcome.

[@jeffreyser]

Take the 100% wand and point it at whoever's going to turn us all into cats.

[@Halosty45]

Best solution, really.

[@KuroroSama42]

Then you immediately lose to one of your opponents... and you also miss out on the chance to just maybe get to be a cat.

[@greekfire7980]

Kuroro Why be a cat when you can be a carrot.

[@timmygreat1230]

Manolis 7733 You umderstand

[@mladen7641]

And nobody is gonna care? Yeah, sure, that makes total sense

[@egon3705]

"To prevent draws, a draw is declared if no hits are scored in the first round"

[@kr4qqen127]

and they are turned into cats.. they'd rather win than become a cat

[@TheNeilBlack]

Also, the rules explicitly say they repeat casting in order until only one is left, but then suddenly only one round happens and everyone is cats after that.

[@placeholdername3907]

@@kr4qqen127 id rather become a cat

[@kr4qqen127]

@@placeholdername3907 out of being a sorcerer, dead, or a cat? are you sure?

[@placeholdername3907]

@@kr4qqen127 with cat i dont have to worry about bills while also enjoying the pleasures of life.

[@DigiDrone23]

In light of the original question, without the "miss on purpose" unstipulated rule, I think you should take the 60% wand and aim it at the 90% guy. The chance of you surviving first round is in (30, 31)% range, while if you take the 100% wand and aim at the 90% guy, your chance of survival is 70%. Thus with the first option, you have fraction of a % bigger chance of survival. But it is true I finished the computations with the first round. Maybe it is better to take the 100% wand after all, since the 100% chance in the 2nd round vs a 70% chance would probably outweigh the fraction of a % bonus in the 1st round.

[@KurtvonLaven0]

It's important to clarify in the problem statement that your opponents know your wand's characteristics in advance.

[@keanureeveslusciousweave]

me (hears the words "wizards," and "deadly duel against 2 rival schools") : *this is the Triwizard tournament all over again*

[@keanureeveslusciousweave]

@@doof339 Yes, but I was referring to the duel in this video, it contains 3 people, just like the one in Harry Potter and the Goblet of fire

[@sankitty1235]

@@doof339 also, it was just a joke

[@Thehomieibrahim]

@@doof339 joke alert

[@jackel6674]

NOOOO CEDRIC

[@nightmode95]

Namjoooon

[@medexamtoolsdotcom]

Anyone else notice that the other 2 wizard schools, the "newt-niz" and "leib-ton", are just newton and leibniz with their syllables switched?

[@FriendlyNeighborhoodsocialist]

nope!

[@kfirarthegamer798]

Just noticed that and was looking if anybody else did

[@andrewcallier9107]

wow cool

[@andrewcallier9107]

monsta pix thx for honesty

[@amishra7292]

Are we geeks for noticing it?

[@exammole4545]

Based on the Maze riddle, does this mean we’re in Marigolds Magical Macadamy?

[@BioniclesaurKing4t2]

(Is being turned into a cat really a loss?) My answer: Use the mountain wand on myself to get the heck out of there. Being serious: Use the 60% wand on the 90% foe. If you miss, she'll attack the other guy before you and give you a second chance at her. If you hit, you have a greater chance of surviving a round against the 70% foe, then target him next. [So that was the second-best option, but you never said in the rules you could miss on purpose, so that's a foul.]

[@0SC2]

Missing on purpose violates the first rule, because it's a spell cast explicitly without the intention of eliminating another person from the duel.

[@hannalowercase5928]

but it does eliminate, not immediately but later on (if you win)

[@FluffyDragonDrawing]

"Each has an (x) percent chance to successfully eliminate an opponent you _aim_ and cast at." Aiming and casting are two separate things. Thus you did not aim with the intent to eliminate them immediately; but you did cast it

[@pmurali325]

Well acutally no

[@markmckittrick2596]

Not quite. The first rule says no casting out of order. You are casting, and you are in order, so it is allowed.

[@josephford2226]

@@markmckittrick2596 He's not talking about the first rule within the plot. He's talking the first rule on the "pause here" screen. It says: "Starting with you, you'll take turns casting spells to eliminate each other until only one wizard is left standing." The argument here is that casting a spell with the intention of missing is not following this first rule. If you don't intend to hit with the spell, then you're not casting a spell to eliminate an opponent. Which is what the first rule says you must do.

[@BradleyWhistance]

Could be a good riddle, but the telling of it needs to be improved. It isn't clear that deliberate missing is allowed.

[@neve6759]

Perhaps guessing that you can purposefully miss was part of the riddle itself?

[@neve6759]

McKenzie Cooley I like the kittens too! So cute!

[@Valientee16]

That doesn't make sense. They try to convince you to pick the 100% with the kitty line. Because otherwise every wizard has a chance to miss. This is a badly told puzzle, on purpose.

[@KuroroSama42]

It doesn't matter. If you consider that the deliberate miss isn't allowed, your best bet is still with the 60% wand. Just look at the probabilities at 4:10 ... their odds are a bit off, but all in the same way, which leaves them at the same rankings.

[@ryanhaining4004]

They could just allow you to "pass" and it'd be very easy to explain

[@user-sx6el5ef4c]

How to win: Get the Noethern 1000. don’t cast any spells until the next wizard gets impatient and shoots out of order. He will be forfeit, and you can banish the other since it’s still technically your turn.

[@glowingskydog181]

You: misses on purpose Random person in the crowd: gets tangled in vines You: 👁️👄👁️

[@jeremyscottgraham]

This is the most ridiculous "riddle" I've ever seen. You can't just make up new rules. In which case, my answer is I sneak a live lion into the arena which I have been training for 4 years prior.

[@henhicktaimon]

they didn't make up new rules. missing on purpose fits in the rules as they are given and is clearly the most effective strategy. sorry you couldn't figure it out on your own champ, maybe next time

[@screem_]

@@henhicktaimon Riddles are meant to be tricky and confusing. People don't listen to the rules properly and then complain.

[@0ffaI]

Why are you guys equating something you can do with the tools you have available to bringing a gun/lion to the arena? This is more like if you decided to kick the opponent in the nuts mid duel.

[@aftonallen2864]

@@henhicktaimon Did you figure it out on your own?

[@henhicktaimon]

@@aftonallen2864 i knew the answer but to be fair i've heard this riddle a lot before in different forms so it probably doesn't count as figuring it out. i'm sure when i was a kid the first time i heard it i didn't get it

[@thebelovedlion2208]

Well if we can bend the rules like this, then you can just bundle up, Get the Noether 9000, use it on yourself, grab your Elytra, use your Fire Flower to propel yourself away from the mountain and back to the stadium, and then you see the outcome! Then use the Master Sword to strike down the other opponents, and you win!

[@timerboom3207]

He speaks the language of gods!

[@riverr9881]

@@timerboom3207 Gods!

[@khodibritton8368]

Hey, Archen.

[@khodibritton8368]

Ya hear that?

[@khodibritton8368]

*woooosh*

[@ash072]

I disagree. The rules do not state that you must stay within the dueling circle, only that you be the last one standing. Take the 100% wand, cast it on yourself, and teleport to the distant mountain top. You can no longer become a target and can pass, since you have no viable targets, and your actions will still lead to an opponent being eliminated. The other two wizards will be forced to cast spells at each other since you are not in range. They also cannot pass because they will become a cat. After the first round, there is a high likelihood that one of the other wizards will be turned to statue or a fish. However, the rules do not state that in the second round (or subsequent rounds) that if both remaining wizards are left standing, they will be turned into cats. That is a first round condition only. When the duel goes to the second round, you will have first turn and will be 100% safe. Since you have no target, you will pass a second time. The first rule states that the duel will continue until only one wizard is left standing and since "passing to work towards elimination" is a viable option, you will be assured a 100% chance of winning. Your 100% wand is unable prevent you from standing as a wizard (as it only teleports you to mountain tops). Therefore if you use it on yourself, you cannot end the duel, only continue it towards their elimination. You cannot target the second wizard, so you cannot end the duel. The second wizard does wield a wand that has the ability to prevent a wizard from standing (by turning them into a fish or statue). However, the second wizard is unable to target you. The only viable options are to target themselves or to pass. Since the first rule must be followed , the option to pass is not able to be applied due to passing will not serve to eliminate you (since your own wand cannot prevent a wizard from standing and therefore cannot eliminate a wizard from the duel.) Since there can be no draw, the only way the duel can end is if the second wizard casts on themselves, eventually turning themselves into either a statue or a fish. You now won the duel.

[@SlimJibby]

how did you not pass out from writing that?

[@survivorofthecurse717]

I know I'm late, but I calculated the odds of the apple basket bonus riddle. The odds are both the same with a 70% survival rate. Although the red basket seems like a hazardous choice, and not one that would matter, at that, you have the benefit of eating less apples for those people who hate fruit, as you have the odds of only needing to eat one

[@sdseals2076]

Wrong, if you send yourself to the mountain you are still not there eliminating yourself. It doesn't have to be stated that you have to be in the building. How can you fire a wand from very far away and outside the building? How can you return? They never said you can return a person with the wand nor did they say the wand can be used far away. In the beginning, they said it was a faraway mountain. From the illustration, it was very cold on that on that mountain. Chances are you will freeze. I won't even get into how the wizards aren't going to target her/himself.

[@ash072]

@@sdseals2076 Incorrect. The rules are very straight forward. Unstated conditional elements are not taken into account. The wands work regardless of where you are at and the rules of the duel do not state you have to stay within the circle. It would be illogical to put conditions not specified into a logic problem.

[@sdseals2076]

@@ash072 Didn't you add in conditions?

[@eclipsewrecker]

Explain to your opponents that your banishing wand is “100%,” and it will banish them to a far off place to die. Explain that if you win, you will immediately banish a rescue party to their location with the necessary provisions, enabling their survival. Explain that you will use your first turn to eliminate wizard 3, and if at any point wizard 2 aims his wand in your direction you will immediately cast your spell, guaranteeing wizard 2’s death and potentially all three deaths. Then reiterate their chances of survival are higher with their cooperation.

[@welcometohell3002]

Take the noether, and use it on yourself. Chop down some nearby trees, and build a house. Use the extra for firewood. Encounter a herd of wild mountain goats, and take up the life of a goat herder. Discover a nearby village, and trek down there every day to trade goat milk, and converse with the villagers. Find a village girl, and settle down with a family. Give up magic, and have a simple, but happy life.

[@emperorampora8771]

i like your profile pic and your name.

[@dylanrobson3802]

So wholesome :)

[@GeeGe.]

I really like this.

[@euttdsiggh2783]

arsenicKatnip that was beautiful i have tears in my eyes

[@davysmith1934]

that's....genius.

[@megaultralegomaster]

Since you can make up new rules, here are a few fun solutions to win the duel. Since the rules state the duel ends when only one is standing, you can sit down to temporarily eliminate yourself. The rules do not state you cannot return to the duel after being eliminated. Option 1: I cast Fireball, targeting the ground near the two of them, eliminating both without targeting either. Neither of them are allowed to cast counterspell since that would be casting out of turn. There is no rule against it, therefore is an option. Option 2: I use the 100% wand to eliminate one of my enemies, and then sit down. I am no longer standing meaning the third person cannot target me. I stand up during my turn at round 2 (see rule 5 stating "end of first round" not start of second) and eliminate the third person. There is no rule against it, therefore is an option. Option 3: I teleport to the mountain on my turn, sit down and then run back for my next and end the third person. The rules state you do not eliminate yourself by casting the wand on yourself, only an opponent. There is no rule against it, therefore is an option. Option 4: Shoot one of the competitors before the duel starts. There is no rule against it, therefore is an option. Option 5: Break both of their knees with the baseball bat 9000 wand. Neither of them are standing, meaning you win. But seriously, missing being allowed should be stated within the rules of a LOGIC puzzle. Rules as written, missing isn't allowed since you are not casting a spell at an opponent to eliminate them.

[@edschramm6757]

I see what you're saying, but I'll just Cast Disintegrate, and with my 3 level dip in Sorcerer, use Twinned Spell. Technically, it's one spell that is being aimed at both. Assuming they are both full spellcasters, then have low enough health for that to kill both before they get a turn. They never said you have to use the spells embedded in the wand

[@jamesbaker2092]

I'm going to bonus action hex, then I'm going to use action surge and cast an Eldritch blast at both of them. If either survives, I'll take the dodge action and cast mind spike each time it's my turn.

[@edschramm6757]

@@JohnSmith-xp9gr "at an opponent to eliminate them". If you fire with intent to miss, it is not directed at an opportunity with intent to eliminate them. Thusly, it's not a valid selection

[@aldar8240]

for option 2, it does say that the last person standing wins the duel, meaning that if you sat down the other person would instantly win

[@FluffyDragonDrawing]

1. You targeted 2 people. Not 1; which is against the rules. 2. If you can do that so can they... so one of them sits down right after their turn and gets back up. 3.The wand is specified to eliminate oponents by that method; aka that method eliminates you. Even if it didn't what's to stop the other wizards from pulling a similar trick. 4.it asks for your strategy of winning the duel. Actions taken before aren't a part of your strategy; and who's to say there won't be a replacement. 5.why would they let you do that. I imagine they'd fight back. This ISNT a logic puzzle; its a RIDDLE. There are differences. One is that your meant to think creatively.the other is a case of math and deduction. You are still casting a spell that would eliminate them if it hit. You simply did not aim.

[@ryanedgerton1982]

Alternate solution: you use the Noether 9000 and cast on yourself. You are then transported far away from the contest and can live out your life as you see fit, armed with the most powerful wand. Yes, technically you forfeit the duel, but you have a 0% chance of getting transformed and can carry on from there.

[@hustlerguy6091]

For the Apple Riddle: It does not matter which bowl I choose. The probability of survival in both the cases is 0.7.

[@coryman125]

Isn't intentionally missing essentially the same as going out of turn though? It's basically just saying "No thanks, I don't wanna go first"

[@Hello-qg4yk]

coryman125 yeah

[@KuroroSama42]

Could they prove that you missed on purpose? Your wand has a pretty high chance of automatically missing. Either way, the answer would be the same. Use the 60% wand and hope to miss instead of missing on purpose.

[@chlorine4567]

@@KuroroSama42 They didn't say it had a chance of missing, but a chance of just not working

[@shavedata5436]

@@KuroroSama42 It isn't stated that the spells fail because they miss. It seems likely that they could always hit their target but have a chance to be ineffective.

[@borisandrews3867]

the difference between not going first and deliberately missing mathematically tho comes from the rules about all being turned into cats if no one gets a hit in the first round, in that if this weren't the case we would have an infinite decision space leading to silly solutions such as everybody repeatedly missing on purpose - so deliberately missing is slightly different cause now there's only 2 goes before the cat transformation as opposed to the full 3 if u just hadn't gone first

[@ajg92]

Wrong. Use the 100% to send 2 to mountain. If 3 tries to attack you, they lose because they attack out of turn. It said still standing, not standing there. If you teleport 2 to a mountain, they are still in the duel, but cant attack because they dont know where they are. Assuming wizard 3 assumes it killed him or something, wizard 3 attacks you, technically attacking out of turn , causing them to automatically forfeit

[@jochedev]

Thought of the same thing (with slightly different logic though). Didn't know why no one stated it before.

[@W._Langman]

Exactly what I thought.

[@Xomeal.]

@@nathalie5683 That was never stated.

[@gkaskavelis]

That's a better answer for me as well. Thank you!

[@mysterysecret6815]

Not exactly. Your win rate is still not 100% as 3 can also just stand there and wait.

[@Jedonai]

If you banish the second Wizard first then he cannot take his turn and the third Wizard is disqualified if they cast.

[@seligfay7497]

This reminded me of one inaccuracy in warhammer 40k dh2. When you shoot, if you miss, there is a 50% chance to hit an enemy or ally near the target. If your ballistic skill is very bad, you can shoot your melee oriented ally and you will have huge chances to hit nearby enemies. Of course, the game master won't let you do that, but it's a funny bug.

[@jessegill9923]

Ted Ed: Did you solve the wizard standoff riddle? Me: Ozo.

[@whochangedyoutube]

If I asked you whether 2 + 2 = 4, would you answer ozo?

[@jessegill9923]

@@whochangedyoutube ozo...wait... ulu

[@whochangedyoutube]

@18ismyfavoritenumber 2011 in another Ted Ed video (the three gods riddle), part of the riddle is that you have to use the words “ozo” and “ulu” to communicate with alien overlords, but you don't know which word means “yes” and which word means “no”. N. gill's comment is a reference to that video.

[@jessegill9923]

​@18ismyfavoritenumber 2011 That is the riddle.

[@vtjag10]

😂😂😂😂

[@Prince_Luci]

“I didn’t ask how close together we were, I said I CAST FIREBALL.”

[@doctorxawesomestop-motion1234]

Please, Thunderwave all the way.

[@me_myselfand_i2099]

@@doctorxawesomestop-motion1234 I believe you mean vicious mockery

[@Hazel-xl8in]

use fireball and only fireball! nothing but fireball! just fireball! just fireball. *just fireball.*

[@FriendlyNeighborhoodsocialist]

nu i cast hunger of hadar

[@impish_snake3526]

Meteor

[@YIPJUNHAOMoe]

For the apple riddle at the end, You should choose which type of apple you like, here's why: For the green apples, there are 60 possible outcomes: 6 = All good =10% 36 = 2 good 1 poison = 60% 18 = 1 good 2 poison = 30% ( there are only 2 poisonous apples, so there is no possible outcome where all are poisonous apples) Since you only die when you eat 2 poisonous apples, there is a 30% chance you die if you eat the green apples. As for the red apples, there are only 20 possible outcomes: 2 = Both good = 10% 12 = 1 good 1 poison = 60% 6 = Both poison = 30% Since you only die when you eat 2 poisonous apples, there is a 30% chance you die if you eat the red apples. Even though it seems that one or the other as a more likely chance of survival, they both have of 30% of killing you. ( This took me longer to type than to calculate lol)

[@vedarao_0]

Your answer is correct but Isn't this a combination (order doesn't matter) and not a permutation so there are 10 outcomes each For green apples: pick 3 apples, 2 poisonous 1 = all good apples 6 = 2 good 1 poison 3 = 1 good 2 poison For red apples: pick 2 apples, 3 poisonous 1 = both good 6 = 1 good 1 poison 3 = both poison Either way probability of death is the same

[@ryfors]

Thank you

[@Depressed_Spider]

My approach looked like this: For the green apples you have to pick two that you don't eat and for the red two that you eat. If both green apples you don't eat are from the 3 in 5 majority, you die, same for the red apples that you do eat, so it doesn't matter which bowl you pick.

[@xavierburval4128]

Here’s my answer: The red apples are simple. You need to pick both poison apples to die. The first apple has a 3/5 or 0.6 chance of being poisonous, and the second one then has a 2/4 or 0.5 chance. Multiply these together and you get 0.3, so you have a 30% chance of dying if you pick the red basket. The green basket is a little more difficult. To solve it, I first split the outcomes into two branches, one where the first apple I chose is poisonous, and one where it isn’t. There is a 2/5 or 0.4 chance that the first apple I pick is poisonous, keep that in mind. For me the die, I need to find the second poison apple in my next 2 picks. Since there is only one poison apple left, it can only appear in one of the apples. The probability that it appears in the first is 1/4 or 0.25. The probability that it appears in the second is 3/4 (because it needs to not be in the first one) times 1/3, or 1/4. Both of these outcomes result in me dying, so the total probability is 1/2 or 0.5. Multiply this by the 0.4 probability that the first apple is poisonous, and we get a 0.2 probability of dying from this branch. But there is also the branch where the first apple isn’t poisonous. If this happens, both of my next two picks must be poisonous apples. The probability of the first one being poisonous is 2/4 or 0.5, and the probability of the second one being poisonous after that is 1/3. Multiply these together and we get 1/6, or about 0.163. Adding this to the 0.2 from earlier, and we get a 0.363 probability of dying from the green basket, slightly higher than the 0.3 from the red basket. Therefore, we should pick the red basket.

[@zoey4846]

@@xavierburval4128 Let's analyze the risk of eating from each basket. Green Apple Basket: The green apple basket contains 5 apples, out of which 2 are poisonous. If you have to eat 3 apples from this basket, the possible outcomes are: - You eat 3 non-poisonous apples. - You eat 2 non-poisonous apples and 1 poisonous apple. - You eat 1 non-poisonous apple and 2 poisonous apples (which would cause death). - You eat 3 poisonous apples (which would also cause death, but it's impossible in this case as there are only 2 poisonous apples). We are interested in the case where you eat at least 2 poisonous apples. There are 3 ways you can choose 3 apples out of 5, which is given by the combination formula `5C3 = 10`. Out of these, there is only 1 way to choose 2 poisonous and 1 non-poisonous apple, which is `2C2 * 3C1 = 3`. So, the probability of this fatal event in the green apple basket is `3/10 = 0.3` or 30%. Red Apple Basket: The red apple basket contains 5 apples, out of which 3 are poisonous. If you have to eat 2 apples from this basket, the possible outcomes are: - You eat 2 non-poisonous apples. - You eat 1 non-poisonous apple and 1 poisonous apple. - You eat 2 poisonous apples (which would cause death). We are interested in the case where you eat 2 poisonous apples. There are 10 ways you can choose 2 apples out of 5, which is given by the combination formula `5C2 = 10`. Out of these, there are 3 ways to choose 2 poisonous apples, which is `3C2 = 3`. So, the probability of this fatal event in the red apple basket is `3/10 = 0.3` or 30%. So, the probability of dying is the same whether you choose to eat from the green apple basket or the red apple basket. Since I love eating apples, I will go for the green apple basket so I can eat one more.

[@Camberwell86]

Basically zugzwang in chess but here you're allowed to pass