The trickiest 1% question: In a room of 100, 99% are left-handed. How many must leave to get 98%?

[@bprpmathbasics]

Math just got important! Which sector of pizza is a better deal? Reddit r/sciencememes kzbin.info/www/bejne/jqGaqqaFrrmYjKs

[@Starchaser41817]

50 people. That stumped me for a hot minute before i realized what happens when you remove a person.

[@richardhole8429]

The bouncer will have had a full day!

[@danijelandroid]

I knew it wasn't 1 person but I didn't expect 50 .😂 But 49/50 will get you 98%.

[@slowfreq]

I realized immediately that just removing a person would result in a non-integer percentage, but it took me a while to realize what else to do. But I'm proud to say I got the answer before he said it!!!

[@avinotion]

I'm glad to see that a lot of people didn't go through the entire process, and rather know or have come to the conclusion that in order to double the percentage of right-handed people, you need to halve the total number.

[@brianwade4179]

I thought about it like this. At the beginning there is one right-handed person in the room. How many left-handed people do I need for there to be 2% right-handed people in the room? Clearly I need 49. Therefore I have to remove 50 left-handed people. I did all this in about 5 seconds.

[@PennyLapin]

yeah, it's easiest and fastest to turn the percentage of right-handed people into a ratio to all people in the room. I thought about it about the same: 1% is 1:100, and then 2% is 2:100, or 1:50. to get from 1:100 to 1:50, you take away 50 left-handed people.

[@eventhorizon853]

yeah, this is the obvious way to do it and shows that logic beats algebra in speed

[@ndrslvn1886]

@@eventhorizon853speed is not the reason you use algebra. It’s because of its reliability and verifiability.

[@erenerbay]

Yeah very clickbait

[@pulsarbeam_1]

yes

[@sassymuffinzzz]

This is the first one on your videos that I figured out immediately. My brain went to one person is 1% in the initial scenario, so for someone to be 2% of the group there would need to be half the total people.

[@slowfreq]

That's a brilliant way of thinking about it.

[@zdhshue]

Percentage = x/ (x+1), set percentage to 98/100 which is = to 49/50=x/(x+1), x ist equal to 49. So 50 left handed ppl had to leave since 99-50 is 49

[@StephenMarkTurner]

The small change from 99 to 98 obscures the large relative change from 1 to 2. This is a good general lesson.

[@Violaetor]

Quick intuitive approach - equation balancing, you want to double the number of right handed people, inversely, you need to half the number of left handed.

[@alexandergutfeldt1144]

You need to halve the total number of people in the room! Your stated approach 99/2=49.5 is a bit brutal and doesn't solve the problem! ( Not questioning your reasoning, you didn't word it right! )

[@Violaetor]

@alexandergutfeldt1144 correct, I didn't want to write an essay. I left out the parts of keeping the total number of people at 100 by converting the lefts to rights, reducing by the desired ratio (accidental time stamp), then converting back with the new group. Thanks for keeping me honest, I lazy math often.

[@Crazy-mx9dc]

I thought about it like this: When you want 100 people with 98% left handed, you need 98 left handed and 2 right handed people. Then I divided both by two so there’s only one right handed person. That left me with 49 left handed people. And 99-49=50, so 50 left handed people have to leave.

[@214000451]

The multi marker skills are impressive

[@Caio_Myguel]

I still haven't watched the video nor read the comments, this is how I did it: 98% = (99-x)/(100-x), which yields x = 50. My explanation for the equation is the following. "99-x" is the final number of left-handed people in the room, x is the number of lefties who left (pun intended. Laugh!). The denominator will simply be the total number of of people in the room, which is one more than "99-x", so "100-x". Now, simply equals that with 98% and solve for x. By the way, the addition of one more comes about because there is a right-handed, airhead strolling about this weird left-handed people congress. Edit: yep! 👍🏻

[@joso5554]

50. Basically the single right handed person is 1/100. For it to become 2/100 = 1/50, the number of left handed must decrease to 50-1=49. So from 99 to 49 is 50 left handed people must leave.

[@jorggradert1854]

Only one person right handed. 2% right-handed = 1/50 so 50 left-handed have to leave the room.

[@e1woqf]

Exactly.

[@teelo12000]

50. Had to pull out a calculator and guess-and-check. Never would have been able to figure that out on the spot on a gameshow.

[@SaucyCinemaFilm]

Go in the opposite direction: start with 1 right-handed person. How many lefties do you need to bring in to the room to get to a ratio of 100:2 (given that the max number of righties is 1)?

[@Kerguelen.Mapping]

5:00 fifty!

[@jamesharmon4994]

This assumes you don't remove the one right-handed person! Then, it suddenly becomes (and remains) 100% left-handed.

[@johnh7411]

@@jamesharmon4994 The original problem says ‘how many left-handed people have to leave the room’.

[@Delfontes]

The gameshow gives you 30 seconds to solve, took me about 15 when I realized 98/99 is still pretty close to 99%... and a short jump to 49/50 is 98%.

[@沈博智-x5y]

to try to solve it within 30 seconds a viable option is 98% = 98/100 reduce this fraction 49/50 luckily the original condition was 99/100 = 99% so removing 50 from numerator and denominator (removing 50 left handed people removes 50 from total) leads to 98% looking at the comments, the 1% to 2% trick is even better (thinking of the complement, amount of right handed people) 1/100 2/100 = 1/50 (so removing 50 from 100) either way, final ans 50.

[@nekogod]

50 people, 99/100 is 99% 49/50 is 98% Kevin of Vsauce2 covered this exact thing albeit with a different premise (something to do with potatoes iirc). You can also look at it the other way round, there is 1 right handed person 1 out of 100 is 1% you need it to be 2% so 1/0.02 (or 100/2) which is 1 out of 50

[@aurochrok634]

50. It’s a simple equation (99-x)/(100-x) = 0.98 . Which simplifies to 0.02x = 1 and hence x=50

[@monroeclewis1973]

I solved it mentally with algebra. The hardest part was remembering the numbers, keeping them in mind. Here ‘s the equation: 99-x/ 100-x = 98/100. It took me more than 30 seconds to do it, though. Still, not bad for an octogenarian!

[@adamsmith6995]

Easier mathematical manipulation if you recast as right-handed percentage. 1 right-handed person in the room with 99 left-handed is 99% left handed or 1% right handed. So to go down to 98%-left is to go up to 2%-right. Equation is almost the same but much quicker to solve since there is always 1 right handed peron and "x" left-handed people need to leave ther room 1/(100-x) = 0.02 Note it is easier if you recall that 0.02 = 2/100 = 1/50 1/(100-x) = 1/50 So 100-x = 50. x=50

[@CoffeeSipper555]

I solved it in 10 seconds: If they are 100 people every person is 1%, half of those and every person equals 2% so they need to be 49 out of 50.

[@_idylicrune_5035]

I love your videos! I’m terrible at math, yet I find so many elements about it (like this) so truly fascinating.

[@benceringbauer9477]

My way of solution was, in the first case for 1 right-handed there are 99 left-handed. How many of left-handed has to leave so the ratio change to 1 right-handed to 49 left-handed (2-98). And you see the answer immediately. Interesting question though.

[@nickcellino1503]

Another problem is asking how to bring the percentage down to 96%. The answer is 75 left-handed people must leave the room leaving 1 right-handed person and 24 left-handed people. 24 out of 25 is 96%. The easier way to calculate this is to concentrate on the number of right-handed persons which is always one. 1=4x/100 which equals 25 so there are 24 left-handed and 1 right-handed so 75 of 99 left-handed must leave the room. In the problem given the equation would be 1=2x/100 which equals 50 so there is 1 right-handed and 49 left-handed (49 out of 50 is 98%) so 50 left-handed must leave the room. This math is easier than what is shown.

[@wyattstevens8574]

What I did was the "what if the roles were flipped" case and continued until 0.9^(100-x) >= 0.01, which gave me an answer of... 55!

[@DeVibe.]

Beautiful!

[@NiceEyeballs]

Bro how lucky am I to search this and only your video came up that was uploaded 5hr ago. Nice

[@Silvar55x]

No need to guess. Just reason how many people you need to have the sole right-handed person represent 2%.

[@e1woqf]

2% means 1 out of 50. That's all.

[@knutritter461]

I immediately realized that1 cannot be true and the reason is due to the decreasing group's size.

[@BleuSquid]

I always come at these by solving for the total first, and the difference second. If we want 98% left handed, then we want to know 100% - 98% = 2% of some number = 1, so solve 0.02*x=1, to find that the new total number of people is 50 (1 right, 49 left). Then subtract, 99 - 49 = 50.

[@yoboidoubleS]

I thought about like this. Basically, if you remove one person, that's -1 for both the total and the number of left handed, which isn't exactly 98% in any case instead of 49 people out of 50 total people. And 99 - 49 is 50 people

[@jp2ric]

As soon as you realise the numerator and denominator in 98/100 both have 2 in common, you can rewrite it as 49/50 and voila!

[@EMC273]

The trick was to not let intuition kick in and remember the definition of probability (favored cases)/(all possible cases)

[@Dexaan]

I figured this out by ignoring the left-handed people (they're up to something sinister anyway) and realizing there must be one right-handed person. How many people need to be in a room to make one person 2% of a group? 50.

[@dentonyoung4314]

Last time I saw that question, it was about a watermelon weighing 100 pounds that was 99% water and the question was how much water would have to evaporate from it for it to be 98% water.

[@johng.1703]

I would think that to go from 1% Right handed to 2% right handed, you would need to half the total number of people, so 50 would need to leave the room so that 1 person equates to 2% of people.

[@testenzgames7752]

My way of doing this was thinking: at the initial case, there are 99 LH and the total is 100, if you remove one LH, youd have 98 LH and 99 total, and If you keep doing this, you will have, no matter what, for x LH, a x+1 total amount of ppl, and since 98% is LH/Total, you can say x/(x+1) = 49/50, which is the reduced fraction of 98%, the you can clearly see that x is 49, so you take 99 which is initial minus the ones who stayed, 50 LH left the room.

[@herbie_the_hillbillie_goat]

My technique was to say, "watch it be something like 50." Worked like a charm. 😁

[@lewisyang8454]

This is like the 99% water in a grape question. You can also do it reverse and find the right-handed people. Since it is 98% left, you want 2% right, and 1/50 is 2%. Then just 100-50

[@thomasdegroat6039]

Immediately realized the trick but couldn’t figure out how to calculate it other than just guessing. Would’ve been way easier if I just realized that 2% is double 1%

[@thisjosiah]

I thought about it as having to have 2% of the population not be left-handed, and that the only whole number less than 100 in population that can have 2% of it gone and still have a whole number is 50, that must have been the answer.

[@Dafunboy_5570]

this felt easy initial: 99:1 final: 98:2 simplified final: 49:1 99 - 49 50 left-handed people left

[@CesarGrossmann]

One (right-handed) person in one hundred corresponds to 1%, one person in X corresponds to 2%.

[@mantasr]

If you allow rounding down it can be fewer people.

[@ShimrraShai]

FWIW this same thing is also the trick behind those funky IQ test problems that go "Sarah is 15 years old and Shane is twice as old as her. How old will Shane be when Sarah is 20?" You have to not forget that BOTH quantities involved are changing.

[@andvil01]

Instead of using the lefthanded you can use the righthanded. The ones that never change. In the room there is 1 righthanded person. If that person is 2% of the total, the total is 1/0,02=50. So to be 50 left in the room 50 have to leave. All left handed. This is the same as the drying cucumber. A 500 g cucumber is 99% water. As it dries in the sun the water conten goes down to 98%. How much does the cucumber weight then? We know the dry matter is 5 grams and never changes. 5 g is 2%. Total is 5/0,02 = 250 grams. Half of the cucumber has dried away. No need for algebra. When working with dilutions always look at the matter that is diluted. That never changes when diluted. It doesn't matter if it is Sodium hydroxide in chemistry, dry matter in a cucumber or a righthanded person "diluted" in a lefthanded population.

[@UncleKennysPlace]

I did it by figuring that 98% is a 49:1 ratio.

[@johng.1703]

it's way easier to look at it from the other point of view, that is going from 1% to 2% of "other / right handed" and to get 1% to 2% you need to half the total.

[@paulhammond6978]

yup. 50 people. I had to write the equation out properly to see it, though

[@akuunreach]

50, 1 right handed, to double that, half the people need to leave After finishing the video: There are 2 simpler ways at looking at this problem. 1 & 99, what do we need to do to make 100 people = 98%, we simply replace 1 lefty with a righty, 2 & 98, and now, we can just remove half, 1R and 49L to maintain the ratio, or 50 people. The other way is as above. We want to make 1% become 2%, since we are doubling, we need to halve. I think these concepts are a little more intuitive, and easier to grasp. I wouldn't be surprised if even mathematicians spit out the wrong answer, or had to give it a bit more thought directly because they didn't look at the 1%, and instead focused on the 99%.

[@Engy_Wuck]

you don't need complicated math ("oh no, there's an x in it") to solve it, if you look at it a bit different: if the percentage of left-handed people drops to 98% then the percentage of right-handed ones increses from 1% to 2%. For the one person te become 2% the total has to be 50 (2% = 2/100 = 1/50). Therefore the number of people in total has to drop to 50 from 100, which means 50 have to leave the room. I've known the question a bit different: a fruit vendor scolds his apprentice: "you let the strawberries too long in the sun, now they are ruined" and the apprentice wonders "why so? The percentage of water in them only dropped from 99% to 98%..." - who's right?

[@robertpearce8394]

This is from a tv quiz programme in the UK. The contestants are asked a series of questions, getting increasingly difficult. The show starts with 100 contestants, and you get one wrong, and you are out. They are puzzle type questions rather than general knowledge. At the end, the remaining contestant(s) get asked the 1% question, that is a question that 1 in 100 got correct. In this case, there was only one contestant who got the answer wrong. There is a time limit of 30 seconds for each answer, which means you need quick thinking. I think that playing along at home, the only 1% question that I got was the sum of the numbers from 1 to 100. It was not asked directly like that, but that was the idea. This is a question that most recreational mathematicians can answer. However, the final question is usually a logic puzzle.

[@-wx-78-]

In chemistry, if you want to double concentration - you should somehow halve mass or volume. 😉

[@paulrobinson270]

I got if from the right handed people. Right handed = 1%. When left handed = 98%, then right handed = 2%. Right handed number does not change, so when does 2% = 1 person. It's when the total is 50. That means 49 left handed people = 98%. 99-49 = 50 left handed people have to leave.

[@mda99das]

I admit I could not do it in the time frame of 30 seconds but you have L/(L+1) =0.98. multiplying out and finding L is 0.98/0.02 which gives 49. Thus 49 lefties and 1 rightie makes 98%. Now the question asks how many lefties need to leave. 99-49 is 50

[@quigonkenny]

You don't need algebra for this one. You just jeed to understand fractions and percentages. 98% = 98/100 --- percentage --> fraction 98/100 = 49/50 --- simplify 100-50 = 50 --- find the difference Given the same starting conditions, this works for any percentage from 50% to 99% inclusive which you can represent exactly with (x-1)/x, where x is an integer from 2 to 100 inclusive.

[@arld93]

an easier way is to think that there is always only one right handed so if one is 1% of 100, one is 2% of 50

[@josephbaker9932]

This is one of those questions where if you try to answer the opposite question it is easier. 1 is 2% of what number? 50. i.e. 1 & 49. (1 + 99) - (1 +49) = 50 people must leave

[@Hdtjdjbszh]

there is a much nicer way to work this out, let x be the percentage in the NOT group. If In the first insance x=1%, and in the second instance x=2% you simply have to ask "x/what = 1% and x/what = 2%" being as we know that the 1% is also equal to one person we can solve 1/100 = 1% and 1/what? = 2% I know it is essentially the same as his formula, but I think it is a simplier way to frame it

[@StephenWightTn]

It's much simpler if you look at the inverse. In the same room, there is only one person. What does the total number of people have to be for that one person to be 2% of the population? 1/0.02=x 50=x to achieve that, 50 LH people have to leave the room.

[@narfwhals7843]

For one person to contribute twice as much percentage you have to halve the number of people.

[@john99218]

Objection! Objection! We will have to remove 50 LEFT-HANDED PEOPLE from the room. You have to be careful not to remove the sole non-left handed person.

[@GolDGreg]

I was just thinking how to double the take away one, which would be divide the total by 2. Instead of 100, it would be 50 take away one, so 49/50=0.98

[@dansidney]

The easiest way to figure this out is simply by turning percentages into fractions. We have 99/100 and we want 98/100 ? Simplify 98/100, both numerator and denominator are multiples of two. 98/100 -> 49/50 And then the answer is immediate.

[@DWal32]

only 1 lefthanded person has to leave the room... the catch is that a righthanded person has to enter, but the question never stated you cant add righthanded individuals to the room

[@BillyKamp]

Its weird but to me it became logical when I asked myself, how do I make one person became 2%? For the left-handed to be 98 the one right-handed guy had to represent 2%, and that means I had to double his concentration in the place, so to double him I would have to cut in have the concentration of people. I

[@SlothfulSage]

For me, at the start, we were already given the number of right handed people to be one and left handed to be 99. So, I said when is 1/x equal to 2% of the people, which gives us the answer of 50. From the 99 left handed people, we subtract 50 from it to get 49.

[@kriz5652]

1/100-× =2% or 1/100-x=2/100 therefore 50=100-x its more easy if you count the right handed guys!!

[@rogerkearns8094]

Yes, I got it. I think it took me about half a minute's thought, so I don't know whether I'm in or out. Interesting puzzle, curiously trappy.

[@jeanrichonez2022]

The weirdest thing in this problem : 99% left-handed population

[@PKua007]

Got it in 2 seconds. But I’m not a genius, I just happen to know this “paradox”

[@foogod4237]

This problem depends on whether you are using rounding or not. The whole problem is specified to only 2 significant digits, so if we use the same precision for all our calculations, it is only necessary for 34 people to leave, resulting in a percentage of 65/66 = 0.984848... which rounds down to 98%. (Why yes, I am a physicist, not a mathematician. How could you tell?)

[@gta4everrr]

I took a slightly different approach. I just assumed there was still 1 right-handed person, who now represents 2% of the people in the room. That means there are now 50 people total, so there are 49 left-handed people. This means you need to remove 50 left-handed people.

[@williamgeorgefraser]

50 left-handed people need to leave the room so that the single right-handed person represents 2% of the people instead of 1%

[@yaskynemma9220]

I did it with the right handed person, we cant remove the only roght handed because left handed would be 100%, so we want to mantain 1 person and make it so 1 right handed person is 2%, so you can calculate that if 2% is 1, 100% is 50, minus the right handed it would be 49 left handed that will stay

[@FBIchan]

Help! Someone! Is it 50? This took me 2 minutes! 98%=49/50

[@alex_ramjiawan]

I just did x/(x+1) = 0.98 to find the number people who had to leave.

[@blockshift758]

I was thinking 3 before starting the video. And when you said that was wrong i paused it and thinked a little more. There is 1 that i needed to double the value in 100 and how do i double the value of that 1. Thats when i unpaused for the solution.

[@tchevrier]

I used a slightly different method. 99 are left handed so that means 1 is right handed. 1 out of 100 equals 1% 1 out of 50 total equals 2%. That means 50 less Total people.

[@sunshinestate777]

Wow that’s really smart. I feel like that observation is the fastest method possible.

[@michaelmccabe-w7u]

That is integer simplicity. If you allow round off up at .5 and down below that the question becomes when does the percentage fall below 98.5 I would have thought that it would be at the midpoint between 48 (exactly 98%) and 99(exactly99%) but it isn’t It falls below 98.5% at 66 people. Why?

[@kyungshim6483]

yeah! I got it right !!! First time .... like EVER !

[@brownro214]

50, 49 lefties and one righty. 98%.

[@simeonsurfer5868]

in my head: 100-99=1, 100-98=2, 100*1/2=50, 1-50=49, 99-49=50, so 50 left-hended need to go.

[@ΙερώνυμοςΚόρακας]

I need that sweater

[@andrewb2452]

I understand the concept but ive seen a few people ask the same question. We are talking about the left handed people, but if you remove half of the people in the room then theres a high chance of removing the right handed people too. I know its irrelevant to the question but its an inconistency

[@Insightfill]

"Only 1% get this right..." I've got a plan; stick 100 people in a room and give them this question... (It's the right-handed person who got it right, isn't it?)

[@Malime-rn3fg]

98% is 98/100, that´s our target, you simplify the fraction and result 49/50 and then you have the answer

[@fannelly00]

Its easier if you do other way. How many people in total you need so 1 perason become 2% . 1÷2% =50 people in total . And the answer is how many people you need to remove so is 100 - 50 = 50 in this particular case is the same

[@UP9724659]

Won't (x-1)/x = 0.98 be faster?

[@MrUberGolfer]

Congratulations, you won the prize for the most complicated answer to a super simple question that is easy to calculate in your head: 1 person is righthanded. How many people must be in the room, for 1 righthanded person to make up 2%? Easy Peasy, right?

[@borstenpinsel]

99L, 1R l: 99/100 If one L leaves, it's 97/98 which is still almost 99% We need the one R person to be 2% and we get there with 1R and 49L. So the answer is: 50 left-handed people must leave

[@matthewdodd1262]

50 people. I find it easier to think of the reverse. If the right handed person makes 1% of 100, how does he make 2% by himself? Having half the total people

[@krakenzback7971]

just think the only way to get 98% is 98/100 or 49/50. Cant be first option cuz if u remove 1 person its 98/99 ≠ 98% so it has to be 49/50. since theres 99 left and 1 right. by removing 50 left, you get 49 left and 1 right = 49/50 = 98%. takes about 10-15 seconds when you think like this

[@HadesTimer]

This is a great question to ask LLMs. They have lots of trouble with it...

[@peter8799]

Nah they solve it without problem

[@dhdtht]

50 left-handers, or 1 left out 1 right in if we are being "creative"

[@sarantis40kalaitzis48]

After 1 minute, the answer is 50 left handed,because the right handed is 1/50=2/100=2%, so left handed percentage is 98%. If the right handed is amongst to those that leaving the room, then for any number of leaving the room, the percentage of left handed is always 100%.

[@JimmyMatis-h9y]

A selection without replacement problem in disguise

[@thegreatbambino3358]

Really? I got this in my head in about 10 seconds.