Child's homework puzzle is baffling adults

[@JonSebastianF]

*Alternative approach* The whole pyramid can be written simply as: 40 = (7 + ★) + (★ + 9) And then you take it from there.

[@seanh884]

That's how I saw (and solved) it.

[@ne9958]

33

[@michaeledwards2251]

I took the approach the LHS is 2 less than the RHS : the heart is 21. Given the heart is star + 9, the star is 12. Heart + star is 33.

[@dflayne]

why are you making this so difficult? It is far easier just to write 40 = (7 + star) + heart. You can go straight to that one, simple equation.

[@74810Eric]

​@@dflayneBecause you can't define the value of ❤ without knowing the value ⭐ since (❤=⭐+9). Simply writing 40 = (7+⭐)+❤ is the same, but a step back. Just replace ❤ with ⭐+9. I get that the question only asks what is ⭐+❤, but finding out each value seems to be realiable.

[@daindreska8206]

It's not a particularly difficult problem, but I definitely didn't expect to see it being given at such a young age.

[@oxedward4738]

It’s not hard, but it is kind of a confusing way to format it and it took me a bit to figure out what the pattern was. Once I realized what it was, it was very easy

[@lmfao3293]

@@oxedward4738 no, u're not 9 yrs old

[@edmx]

To be fair, most adults are baffled by splitting a restaurant bill.

[@Patrik6920]

Lmao 😂

[@calholli]

Women.. 🍵

[@timothyvenable3336]

Haha so true

[@mickdavies5647]

2☆ = 40 - 9 - 7 This is easier than splitting most restaurant bills! 😂

[@ambhaiji]

@@mickdavies5647 yeah but coming up with the idea of the 2⭐is the hard part for these adults.

[@ogi22]

To be fair, that REALLY is a difficult problem for a 9yo. It requires figuring out a way to solve a problem by substitution.

[@Pikachu132]

Nah, this is a nice age-appropriate puzzle for a 9 year old. Maybe not one that should be assigned as homework, but wouldn't be out of place in a childrens' puzzle book with matchstick puzzles and other logic excercises.

[@ogi22]

@@Pikachu132 Oh, I didn't mean it's too difficult when someone likes solving puzzles. Kids are usually amazing at such things. Under one condition - fun. That's a general school problem. It takes the fun out of learning. And we adults are masters in making really fun things into teadious tasks. I was lucky to have a dad, who understood the concept of problem solving and explaining things in simple terms. Many years later I found out it was a core of a Feymnan's technique for learning very complicated things - just try to put it in simple terms and use examples from everyday life. As any student, I suffered from a chronic lack of cash, so I tried to earn a bit by giving private tutoring in math and physics. I still remember one girl who was about to fail her classes in mid school. She hated both subjects. And after a month of tutoring, when she finally got her passing grades, she told me: "you know... Now I don't hate math and physics so much". The only thing I did was to explain those problems a bit differently, using examples she could relay to, showing the method of chopping a big and complicated problem into smaller and easier parts. Kids are great at problem solving. They just need adults to stay away from making that learning pitiful 😉

[@llaffer]

The way I did this was notice that the way the pyramid was built, if we call the 3 numbers on the bottom x, y, and z, the number shown at the top is (x + 2y + z). I could then use that to solve for star immediately. Once we know that, we can solve for heart by adding the 9, then add the two together. I got 33.

[@DiamondCake2]

This was my method. I realised that the sum of 40 was obtained by adding the bottom left/right values once, but the middle number is added twice as you go up the triangle. Once you’ve worked out the bottom number the rest is trivial.

[@bs31415]

This was my approach as well.

[@anim8edpatrtiots803]

Same instinct here

[@_ZAOB_]

Me too

[@gristor]

Same here :)

[@xyzct]

At a coffee shop my bill was $5.25. I gave the barista a $10 bill and a quarter. It was like watching the Hindenburg 2.0

[@lordd007]

Uhh they don't want the coins either 😂 maybe they were hoping to give you a bunch of change that other people keep giving them 😂

[@ChrisOBrien666]

That happens to me all the time. The cashier looks at you and usually replies with something along the line of that’s too much money. Bill comes to 16.95 and you give them a 20 and a two dollar coin (I’m in Canada, we don’t have dollar bills, we have one and two dollar coins), instant deer in headlights look. Just give me back a 5 dollar bill and a nickel. I don’t think they actually know how to use the cash register, they just hit the Cash key like giving exact change and they can’t do the math in their head. Just enter $22.00 before you hit the Cash key and the machine will actually show you how much to give back.

[@rudeq86]

the barista didn't know how much the tip was and his/her brain shortcircuited

[@joepiazza3756]

I gave a teenage worker at an amusement park $20.75 for a $5.75 Icee. Me and the whole line stared at her doing mental math. I got my Icee and $25 back in change.

[@Ironoclasty]

@@joepiazza3756 Sorry, I've got to say it: that's not okay. Maybe help someone instead of taking advantage of them.

[@CharlesBallowe]

My first instinct was "40 = blank box + heart" and "blank box = 7 + star" so ... "40 = 7 + star + heart" and then "33 = star + heart" which is the answer. Apparently this was the "clever" answer.

[@joe_lwrnc]

Yeah I did the same thing

[@colors6692]

Everyone did it that way bro...nothing clever about that solution🤣🤣

[@CharlesBallowe]

@@colors6692 right. The video waited until the end to cover the obvious path. I'm not sure if there's research suggesting that the other paths are more likely to be found in grade school math homework or something else. I didn't feel it was clever - often the videos actually do show at least one path I didn't think of, this one felt like it was stretching to fill time.

[@Yu-Gi-Oh36508]

​@@colors6692yeah he put clever in quotation to show he doesnt think thay but thats what they said

[@neilgerace355]

@CharlesBallowe How about "40 = blank box + ♡" Therefore ♡ = 40 and ☆ = 31. Isn't this logical too? There's no reason to assume that the blank box isn't really blank.

[@MrGhosta5]

The hardest part was figuring out what the question was actually asking me to do. At first I thought it was asking me to solve a ratio but then realized it's just a really badly written substitution problem. Math used to be straight forward and would just ask you to solve for X: 40 = (7+X) + (9+X). Now we have to decipher what the question is even asking us to do.

[@NerdByAnyOtherName]

My logic was that 7 and 9 are two apart, and both 7 and 9 are being added to the same number to create the middle numbers and therefore the middle numbers must also be two apart, and the only way to do that to get 40 is 19+21 so the middle row is 19|21 and the rest of the puzzle solves itself from there.

[@J0rdan069]

Same, but I am way worse at explaining my thought process.

[@myyoutubeid5451]

Ywp this is simple way, no algebra required

[@EnriqueAThieleSolivan]

True. Only sum, and subtraction are needed.

[@giantchook3368]

That’s how I did it.

[@craigising]

This is also how I achieved 33.

[@craigstephens1995]

My initial approach was that the numbers in the middle row must be 2 apart (9 - 7). That means the blank must by 19 and the heart 21 in order to get 40. Then star is 12 and the solution is 33.

[@quantumgaming7643]

this one is quite easy ngl

[@NabeelFarooqui]

It's for 9 year olds

[@doge9737]

@@NabeelFarooqui lmao

[@lukasjetu9776]

true, solved it in around 30 secs

[@wasikancb]

Solved it in my head before clicking on the video

[@lukasjetu9776]

@@wasikancb same

[@Xeroph-5]

As my old maths teacher said: "A lot of things are just quadratic equations in disguise."

[@davidreid7293]

Simply 40-7-9= 2 x star. So star= 12 . Rest follows.

[@florianmoosbrugger5177]

This was also my first idea...

[@spitalhelles3380]

yeah, but what is 12+9? not so easy anymore, hm?

[@R0bot4]

@@spitalhelles338021, and 7+12 is 19 and 19 + 21 = 40

[@whlee9382]

@@spitalhelles3380holy that’s hard

[@2righthands816]

@@spitalhelles3380 129, ez!

[@coreywest2872]

The way I did it was the 2 numbers that add to 40 must have a 2 digit difference (because of 7 and 9) therefor must be 19 and 21. The rest is pretty straight forward

[@TravisGn02]

I just used the fact that blank = 7 + star, to get to 7 + star + heart = 40. Meaning that star + heart = 33 I didn't bother working out the individual values at first but when I did I just used the 7 and the 9 to know that the heart and blank have a range of 2, meaning that they are 21 and 19 respectively. Then it's pretty simple to work out that the star is 12

[@maxhagenauer24]

@TravisGn02 Even easier, you don't need to know the 9 at all, it is pointless in this problem because you only need to look at the others.

[@Tiqerboy]

The kind of problem that leaves you wondering if there's anything more to it?

[@gswcooper7162]

@@maxhagenauer24 The 9 isn't completely pointless...just mostly. ;) While 7 + star + heart = 40 gives you star + heart = 33, without that 9 there you'd never be able to determine the individual values of star and heart.

[@maxhagenauer24]

@gswcooper7162 Yes but the question was the sum of star and heart, you could find it by finding each individual values, in which case you would need the 9, but you don't have to. That's what I mean by pointless, it's not needed.

[@TravisGn02]

@@maxhagenauer24 Me working out the individual values was just an extra bit that I did for fun, I thought that was fairly obvious to be honest. If you don't care about the individual values then just don't read my final paragraph lol

[@yorelyoung6407]

The total is 40. This means that you need to figure out what number can be added to 7 and 9 to make two numbers that equal 40. 7+12= 19 9+12=21 19+21=40 And this is based on the rules established at the start before his explanation.

[@dumptrucc2458]

Easiest MYD problem by far

[@andrewhooper7603]

don't take this w from me

[@petasmith6258]

I agree, got it straight away 😮

[@Boostthenoob]

True, I did it in my mind easily

[@chazbo2672]

Good for us or more particularly, me! I’d like such an easy MYD problem more often than… hm, how many years has it been?😅

[@theroyalmediator2658]

​@andrewhooper7603 It's all good. We have to take the W's where we can get them.😂😂

[@kziadie]

I approached it from a logical more than algebraic angle. Although the top number is the sum of the two below it, those numbers are built on the bottom row. Star is included in the sum for both middle row numbers so the top number must be equal to the lower left number plus the lower right number plus 2 star(since it is a component of both middle row numbers. Hence 7+9+2star=40. From there it is simple.

[@verkuilb]

I used a different method: I noticed immediately that the triangle is Pascal’s Triangle-so the top sum is equal to the bottom left plus the bottom right plus double the bottom center. That immediately solved the star to be 12. The heart is then 12+9. The Pascal’s Triangle method works even if additional rows were added to the bottom of the triangle.

[@wizardsuth]

Next you'll be telling me the numbers in the triangle can also be used as the coefficients of polynomial equations.

[@Kyrelel]

I would be impressed, if he hadn't told you that at the start of the video.

[@sunstreak132]

I didn't know what Pascal's Triangle was until I read this comment, but this was the exact method I used while I was looking at the thumbnail. I wanted to know the relationship between the filled triangle's top number and bottom numbers, and applied the solution I found to the problem triangle to find the solution. I reverse engineered Pascal's Triangle without knowing.

[@collingallaway5541]

I think I solved this is a pretty simple way: since we know that the middle number is the sum of the 2 numbers below it, I noticed that the top number would be the sum of of the outer numbers on the bottom row + 2 times the middle number. In reverse you just subtract the 2 outer numbers from the top (40-7-9) to get 24 which is 2*12. Thus the bottom middle number is 12 and can be used to calculate the remaining values

[@ErikBongers]

As others also noted, but I like to phrase it differently: All values come from the bottom and simply trickle up. However the middle value trickles up twice! So 40 is the sum of the bottom values, with the middle value added twice. This quickly gives you a middle value of 12.

[@GodwynDi]

That is how I solved it as well. And then once you have that, finding

[@wobaguk]

My immediate thought was this is some simple simultaneous equations, which is not to say I would expect that of a 9 year old, but the baffled parents? I think so.

[@charliethunkman]

There is some ax^c+by^d+e where x increments on the horizontal axis and y increases on the vertical plane, but it isn’t clean cut in any fashion, and very unlikely would the solution be an integer if you were to find a,b,c,d,&e in this equation that works.

[@angeldude101]

Each cell is the sum of the two below it. So 7 + x = y, 9 + x = z, y + z = 40. We only need to know x + z, so sub (1) into (3) for 7 + x + z = 40 and subtract 7 from both sides for x + z = 33. We don't even need to know what x or z are.

[@ujasshrestha4418]

Heart is 21, star is 12

[@estebangutierrez160]

That's what I said.

[@dontworrybehappy5139]

Another way to solve for 9 year olds who don't yet know algebra is to notice that in the middle of the pyramid the number on the left will always be 2 less than the number on the right since 9 is 2 greater than 7. Then you need to find two numbers which have a difference of 2 that add up to 40 which leads to 19 and 21. From these numbers you subtract 7 from the left and get 12 or 9 from the right and get 12. So star is 12 and heart is 21 and the sum is 33.

[@popogast]

That's exactly my solution.

[@MahouShoujoNobue]

For simplicity of explanation, let's call the star x, the heart y, and the blank space z. So, z=7+x, y=9+x, and 40=y+z, which can also be written 40=(7+x)+(9+x), which simplifies to 40=16+2x, which we can solve to 24=2x and then to 12=x. Now that we know x is 12, we can find that y is 21 (12+9) and z is 19 (7+12), and thus x+y (or star+heart) equals 33. I don't even teach math, I'm an English Language teacher.

[@thunderatigervideo]

The fact that you don’t need to know star or heart individually actually makes this really easy. Blank (x) is 7 plus star, which then add to heart to make 40. So heart and star just have to make up the leftover after 7.

[@Tredenix]

I imagine this is why the box was left blank instead of filled with its own shape - on an actual question paper it'd help to visualise this by drawing lines from the 7 and the star through that middle-left box up to the 40, along with one from the heart.

[@jsmariani4180]

I can't answer any of his puzzles correctly, but this one was child's play.

[@joemyk]

Star = 12 Heart = 21 Edit: Sum = 33

[@Urielthalas]

You can also rework the problem into a word problem by saying, "What number, when added to both 7 and 9, results in the sum of those numbers equaling 40?" And from there you can set up an equation.

[@TheAstronomyDude]

I think they're pretending to be baffled just to get views on their posts.

[@FingerswithStyleAcoustic]

Someone see my solution: What i did was kept the blank space and heart as 20 and 20 respectively. Now ,star is common in both 7+☆=blank and 9+☆=♡. Therefore the difference between the blank and heart should be 2 as 9-7=2. So i subtracted 1 from 20 and adde 1 to 20 to get the values of ♡=21 and blank=19. Then i got ☆=12. Therefore,☆+♡=21+12=33. Simple!!!!!!!!!

[@pdurys]

My way of thinking without "complex" calculations

[@niroshanaperera7330]

That was pretty simple honestly, 40-(7+9)=24, so we get 7+12+12+9 = 19+21 = 40 So we get 21+12 = *33*

[@DekonR]

That's how I did it too. Nice to be able to do one of these in my head.

[@2kadrenojunkie]

i took what seemed to be the most straightforward approach. first thing i thought of was to add the two bottom numbers and subtract that from the top number then divide that by 2 to get the star. then all i had to do was add the star to the bottom right. there are a lot of different solutions to this as you said. my thinking was that since i noticed the same number was added twice, and no other arithmetic operators asides from addition seemed to be used, i could ignore the middle row entirely. and since i already knew the pattern i just followed it to get the heart and the blank space.

[@Maninawig]

Adult: I never used algebra in real life! Kids: it shows.

[@mjbull5156]

This barely qualifies as algebra. It is more an exercise in recognizing the relevant unknown, and setting up the equation to solve for it. The heart is a red herring that looks important because the other 2nd row box is blank, but it is not. I think that is what is tripping people up.

[@Maninawig]

@@mjbull5156 I was also talking more about the mentality. In my experience, those who gloat over the fact they "never used algebra" also refuses to do any form of equations through pattern recognition. One example I use is that a parent buying sheet cake for their children's party. To make sure you have enough, you need to make sure the number of available pieces at least match twice the number of attendees (as you should assure 2 pieces per person). This can be expressed in an algebraic formula of X=2y/z. However this algebra often occurs without the person even thinking about it. If I recall my psychology, this would translate into them only seeking pattern recognition with their delta brainwaves (surface memory recall) instead of their beta brainwaves (focus), which is the same reason people get caught by simple logical problems like how to spell simple words.

[@bilson7523]

Interesting, I don't recall ever doing these. Took me awhile to figure out the rules pausing at the start. My approach went back to my old-school engineering days: 2 unknowns -> Create 2 equations. I did 7 + 2 * star + 9 = 40 and 9 + star = heart. Use the first equation to get star = 12, second equation to get heart = 21.

[@jwbjerk]

I figured it out by realizing the bottom row was essentially: 7+star+star+9=40. And that means 40-(7+9) = 2x star.

[@Dagfari]

My first instinct was to notice that the number on top is the sum of the middle level, and the ones in the middle are the sum of the bottom level with the middle number twice. So 40 = 7+2x+9 40-16=24 24/2=12. Star is 12 and we can just work upward from there. 9+12 is 21, and 7+12 is 19. 21+19=40.

[@huzefa6421]

37 secs ago ?? This is literally the earliest i have ever been on any video Edit : I used the 1st way but in the reverse manner so that I get 21 and 19 faster ... I started with 25, 15 and then found out that ♡ = 21 and ☆ = 12 ... thus 12 + 21 = 33

[@TravisDoesStuff]

Same

[@Cruzin105]

I tried this before watching. My thought process: Left triangle gives rules for calculation: - bottom right + bottom middle = middle right - bottom left + bottom middle = middle left - middle left + middle right = top Using that: - 40 = blank + ❤ - blank = 7 + ⭐️ - ❤ = ⭐️ + 9 Therefore 40 = 2⭐️ + 7 + 9 2⭐️ = 40 - (9 + 7) 2⭐️ = 24 ⭐️ = 12 If ⭐️ = 12, ❤ = 12 + 9 ❤ = 21 Then ❤ + ⭐️ = 33 (Also Blank = 19)

[@rayraythebrew2863]

Easy enough to do so in your head. Just a small system of equations

[@blacklight683]

(7+S)+(S+9)=40 2S+16=40 2S=24 Star=12 Heart=9+12 Heart=21 H+s=33 indeed

[@jackychanmaths]

star is just (40-7-9)/2 = 12 heart is then 9+12=21 so 33

[@bkm83442]

An easier way to think about it is that the top number is always the sum of the bottom row, counting the middle number twice. So 7 + 2x(star) + 9 = 40 so (star) = 12.

[@Georgggg]

(7+✡)+❤ = 40 ✡+❤ = 40 - 7 = 33

[@otakurocklee]

exactly. The 9 is completely irrelevant to the problem.

[@jimi02468]

@@otakurocklee 7+✡+9+✡=40 ✡=12 9+✡=21=❤ ❤+✡=33

[@AndrewBlucher]

Wrong ⭐

[@craigsaunders7037]

@@AndrewBlucher Is this getting political. If it's going to be a maths war, I'm backing the ✡.

[@AndrewBlucher]

@@craigsaunders7037 Math is not political, it's factual.

[@devondevon4366]

answer 33 Notice in the second row that the number to the left (6) + the number in the middle of the third row (4) + the number in the right of the third row (3) = 13 In contrast, the number to the right in the second row (7) + the number in the middle of the third row (4) + the number in the left of the third row (2) ALSO = 13 The question is similar to the latter (7) + (4) +2 = 13, but two unknowns are in the place of 7 and 4. Hence, a + b + 7 =40 a + b = 40-7 =33 answer

[@MB-ny6is]

40=blank+heart blank=7+star Therefore: 7+star+heart=40 Subtract 7 from both sides Star + heart = 33 Easy 😂

[@LayoffGaming]

A quick adjustment when using the guess and check method: After your first guess, the remainder of the total of the middle values subtracted from the top value, divided by 2 is the amount needed to add (or subtract) from the bottom number. Your example = (40 - 18) / 2 = 11 , so 11 + 1 = 12

[@otakurocklee]

Huh? Why such a long video for such a simple problem? 7 + star + heart = 40. star + heart = 33. The 9 plays no role.

[@guypanton8341]

I like your solution, but. Clean.

[@engi_games]

That’s, not how algebra works

[@guypanton8341]

@@engi_games What? He’s doing a KZbin comment, not algebra. Understanding basic algebra is only one requirement for understanding the comment.

[@jamesdlin7]

@@engi_games The blank space is clearly (7 + star). Therefore ((7 + star) + heart) = 40. Subtract 7 from both sides, star + heart = 33. How is that not how algebra works?

[@martinschalken7583]

Just saying star + heart = 33 is not the final solution. You still need the 9 to solve for them individually.

[@AinsDefcon]

Solution: (40−9−7)/2 = ⋆ (After that, the rest is self-explanatory.) Explanation (Pattern): Lets look at the first triangle. In the bottom it was 2, 4 and 3. We understand that 2+4=6, that 4+3= 7 and that 6+7=13. By doing this we actually used the "4" two times. Therefore we can write it as 2+4+4+3=13. If we invert it we can see that 13-2-3=8 witch we can divide by 2 (since the middle-number is used 2 times), which gives us ... 4. Utilizing pattern recognition, i think this solution is more straightforward. Am i wright or wrong?

[@trapdoorspringfieldmodel1888]

This is a problem that should not be given to kids. All it will do is result in frustration, turn them off to math, and is really just a waste of time.

[@rndmevil]

7 and 9 are separated by 2. Therefore the resulting numbers in the middle row, being the sums of each number, added independently to star will be separated by 2. I divided 40 down the middle and removed a 1 from column 'a' and added it to column 'b'. I then subtracted the corresponding numbers from the bottom row to solve for star.

[@HolySoliDeoGloria]

In about 7 seconds from the thumbnail. I'm trying to figure out what was supposed to be so baffling about this.

[@michaelsorensen7567]

Possibly if the pyramid rules weren't explained in the problem?

[@AndRooooooo]

@@michaelsorensen7567The "rules" are obvious by examining the completed triangle though..

[@RichardReifsnyder]

The puzzle is solvable with basic algebra, but the parent might have assumed the teacher wouldn't possibly throw an algebra problem at a third-grader, and was looking for something even simpler.

[@Llortnerof]

@@AndRooooooo If you realise there are rules to it, which somebody who hasn't been dealing with this in years well might not. Overall it's a case of poor presentation. The problem itself is pretty trivial.

[@jordanleighton6893]

At first I tried to make this a trinomial, realized that it was way over complicating what could be phrased as 2x+7+9=40

[@AndrewBlechinger]

If a 9 year old was given this math problem, they would be exceptionally gifted. I had to set up a system of two equations in two variables to get it.

[@tariqomer4678]

Gifted? Maybe but you don't need to make 2 equations 7 + ❤ + ⭐ = 40 ❤ + ⭐ = 33

[@rightwingsafetysquad9872]

For a 12-13 year old perhaps not. For a 9 year old to figure that out would be exceptional.

[@imp4209]

@tariqoner4678 I regret to inform you that what you have replied is, indeed, 2 equations. I would still consider this problem easy for a 9yo, it's just so simple.

[@rightwingsafetysquad9872]

@@imp4209 dude, what kind of Xavier school for gifted children did you go to? The average 9 year old is still trying to wrap their head around fractions and decimals being the same thing. The word 'equation' has probably never even been said to them.

[@tariqomer4678]

@@imp4209 Oh I haven't noticed lol.

[@alexanderkuhn1335]

To be honest it is absolutely obvious that the middle base entry enters the total sum twice so this is something you solve in less than a minute as 40-16=24.

[@KiloOscarZulu]

Having a blank cell is misleading. We assume that there is a number there, but we shouldn't be forced to assume anything. The question needed to put another symbol there just to indicate that it is not blank.

[@gavindeane3670]

Well the question is meaningless and unanswerable without a number there. I don't see why we're not allowed to assume that the question is capable of being answered.

[@tanelkagan]

The rules were explained - each number in the top and middle rows is the sum of the two numbers below it. Therefore for the box to be blank (i.e. have a value of zero) the bottom middle box (⭐️) would have to contain -7 (negative 7). Which is fine, since negative numbers have not been excluded by our rules. However, you must then follow that through, and applying those rules, 🤍 would have to be 2. If "blank" and 2 are added, we naturally get 2, not 40, so "blank = 0" is not the solution. In other words, there is no "assumption" being made here and nothing is misleading. The rules are clear and if you hypothesise that the blank box really is blank, and test it, it fails the test. That's entirely consistent with the methods in the video, and other methods in the comments.

[@AlexHeisEngholm]

Maybe the blank space could be (sum=15)+8 so the pyramids can have the same rules with the first row 1+. Star can be 8 and heart is 17. When the space is truly blank, anything is allowed, which is my thought.

[@marcfruchtman9473]

Not sure what a "formula" would be for this, but I am going with (7+X) + (9+Y) = 40. Then I solved by subtracting out the 7 and 9 to get X+Y = 24. I then took 24 and divided it evenly for each variable to get X = 12, and Y =12. Therefore Star = 12. This gives a bottom row of 7+ star + 9. Since Star is 12, Empty Space becomes 19, and heart becomes 12 + 9 = 21. Lastly 19+21 = 40.

[@davidjessop2156]

Way too long for a trivial problem

[@stigmontgomery7901]

Maybe because MYD was exploring other solutions?

[@davidjessop2156]

@@stigmontgomery7901 oh I always appreciate the “here’s three ways” as sometimes seeing a different solution approach helps for a completely different problem, or just understanding how people can see the world differently. But as commented elsewhere the top number is left + 2*middle + right of the bottom row. In this case I’m not sure other approaches added much insight.

[@warny1978]

If the botton row is x y z. Then the middle row is x+y y+z and the top row is x+2y+z In this case x=7. We can also guess directly the second row. If we substract the first member with the second, we get : (x+y) - (y+z) =x-z.

[@RJFlute]

I'm baffled by where the confusion was.

[@milanstevic8424]

I did this in 10-15 seconds without watching the video (I stopped at 0:35). I thought it would be harder. But then I saw some fantastic comments overcomplicating this or confidently coming to a solution that is not 33. Now I'm baffled.

[@bobross7473]

@@milanstevic8424I was around 12 when I learned system of equations, and on top of that I was ahead of my peers. This question definitely isn’t for 9 year olds.

[@milanstevic8424]

@@bobross7473 Yes I can agree with that. Maybe for naturally gifted or trained 8-9 year olds, but not in the general case. There is a lot of knowledge I'm taking for granted, I'm in my 40s.

[@Jivvi]

​@@milanstevic8424 I did it about that quickly just from the thumbnail. I'm curious whether the rule of each number being the sum of the two numbers below it was actually given as part of the problem, because it seems trivial to work that out from the first given triangle.

[@milanstevic8424]

@@Jivvi I like to imagine this being published as a newspapers puzzle, like sudoku, but I'm probably wrong and it's surrounded by all kinds of unfun equations that follow the same kind of semi=textual format, in some school almanac.

[@Zetact_]

Trick question, there is no variable present on the second pyramid for 7 + ★. That is to say, you can disregard that cell. Therefore, ♥ = 40 and that means ★ = 31, and ★ + ♥=71.

[@eds1942]

71 is the answer. Every any other answer would mean that you either changed the rule or just assumed that a box of nothing could mean whatever.

[@milanstevic8424]

why tho?

[@eds1942]

@@milanstevic8424 Because the mid-left box holds no value. So you can’t just arbitrarily put things in it. Whereas the other boxes (and top triangle) have values. Three contain known numbers. And two hold a symbols as place holders of a numbers yet unknown, which we know because of the example, the rule, and the question.

[@milanstevic8424]

@@eds1942 That makes no sense. The first pyramid is intended as the clear set up for the actual problem. It shows exactly how the problem should be interpreted, and there are no special rules about the empty box, apart from the classical assumption that all empty boxes have to be filled, just like crosswords or sudoku puzzles. In fact all three boxes likely would've been empty, it's just that the question *labels* the right and bottom ones with symbols so that it can ask for their sum. How else would you know which boxes to sum. Your mistake lies in the assumption that these symbolic labels are always exclusive with the values (as symbolic substitutes), without any evidence to back this up. Whereas a triangle, cross, and seashell (i.e.) could've been labels to valued boxes as well, if only those were needed. Thus, if the question asked for cross + star + heart (with the cross printed in the top box), the solution would have been 73. In short, these symbols do not stand in place of values (like variables), they're just labels to easily identify the specific boxes.

[@gavindeane3670]

Let's assume that the mid left box really does contain no value. You still have 2+4+7=13 in the left hand triangle and 7+star+heart=40 in the equivalent boxes in the right hand triangle. You don't need to even consider the mid left box to get star+heart=33 here.

[@milanstevic8424]

@@gavindeane3670 True. In this case it doesn't really change the outcome. But there is no reason to assume it should remain blank. Usually these kinds of problems are accompanied with a prompt to "complete the diagram". Regarding the symbols these could've been short line indicators pointing at the boxes, with the symbols printed on the pyramid's outside, clearly denoting they're meant as labels. All of this falls under the categories of notation or visual presentation of the problem, not the problem itself. Imagine if every single crossword puzzle had a full explanation of crossword rules so that the solver won't be mislead into thinking that the blank boxes are supposed to be left blank. Also we should make sure people understand what is meant by "box", not to mention that digits and the meaning of numbers could also be a problem if left undefined... What if I consider the values as written in a hexadecimal base? So many possibilities and quite ridiculous.

[@mittfh]

Quickly spotting the logic, I split into the constituent equations, substituting X, Y and Z for the unknowns. X + Y = 40, 7 + Z = X, 9 + Z = Y (7 + Z) + (9 + Z) = 40 16 + 2Z = 40 40 - 16 = 2Z 24 = 2Z Z = 12 Double check: (7 + 12) + (9 + 12) = 40 19 + 21 = 40 So Z + Y = 12 + 21 = 33. Variations on this, with a taller pyramid, appear in many local newspapers in the UK, typically advising readers to try it in their head before writing down the numbers.

[@cristinacu2286]

I just brute forced it lol

[@reagansido5823]

I was looking at the thumbnail and kind of quickly realized that 2 and 4 are below 6, and 4 and 3 are below 7. Once I got the pattern from that it was simple. I added 7 and 9 to get 16, then added 24 to get 40. and since the number at the top will be the bottom left, bottom right, and bottom middle (times 2) I could solve for star as 12. (or half of 24). after confirming what I had deduced, I then solved for heart being 21 (12+9) and from there, star + heart = 33 I'm pretty happy with myself for solving this.

[@ManuFortis]

Pausing at 0, I think I solved it without any extra instruction. Star is 12, and heart is 21. Answer is 33. If correct, I based it off of the first triangle, where 13 can only be added up to by using a corner piece, the middle piece, and the opposite side piece of the corner piece to get the top piece's sum. So 2+4 is 6, +7 is 13. And 3, 4, 6 is also 13 from the opposite side. The middle sections are found by adding the left corner and middle bottom together to get the left middle piece, and same deal with the right side. So now the star and heart. Work backwards. 40 - 7 is 33 (irony?) 40 - 9 is 31. So we need 3 numbers that fulfill the missing parts of that missing sum. Since we know that the corner pieces must be started with, and the middle rank is (seemingly) always high in number than the bottom rank, then the bottom rank can't have a very high number in the middle. But which side to start with? Since we are missing all the 'middle pieces' so to speak, we start with the left side. Why? Because all we have to do is ask ourselves, "what number allows us to split the 33 up so that the bottom number is still going to be lower than the middle rank numbers?" Well, it can't be 8, because that would be lower than both the corner numbers, and the middle bottom of the left triangle is larger than the corner numbers. So it probably needs to be larger too. So it can't be less than 10. But how to find out if it's the right number? Easy. Add the 7 to 10, to get 17, then add 19 (9 +10). If you get 40 (you won't), you got the right number. It was not the right number, the result is 36. So we're missing 4 digits somewhere in that chain. Okay, let's add 2 then, because 1 probably won't be enough. So now it's 7 + 12 = 19, and 9+12=21. Sum is 40. Okay, so we have the star, and the empty space filled. So now the heart. Well, 9+12=21, so heart must be 21. 12+21=33 This might not be the 'right' way to do it, but I got the right answer, right? This took me, maybe 3 minutes to solve.

[@TheLunarDawn]

Found an alternative method that a 9-year old could use as well: We can assume that the corners (7 & 9) are still a part of the top, (40) so we could simplify by combining the bottom corners into (16) and subtract it from (40) that will leave us with the value (24) to be used as various possibilities for Star. We could brute force it and count down rather than count up, but we could also test by distributing the value equally across the Blank and Heart, halving the value for (12) for the same conclusion of [33]

[@dradux2079]

An alternative approach is to think how to sum up to 40. The equal share would be 20+20, but this would require the two bottom corners to be equal. They have a distance of two and this distance needs to be kept in the middle row, because both will get added the exact same number (the middle bottom field). Creating the gap of two leads to 19 + 21, so we already have heart. And from there getting star is easy.

[@xSaraxMxNeffx]

im pretty sure i got there the hard way. the second layer of spaces on the example were left=x+y and right=y+z meaning on the problem pyramid left=x+star and right=star+z then, since half of 40 is 20, but the difference between 7 and 9 is 2; i shifted the split and plugged in 19 and 21 19=7+star becomes star=19-7 which is 12 doing the same with 21 gets you 12 as well, so we know that is correct. 12+21= 33 pretty good for basically being unable to do arithmetic in my head most days.

[@GaborJavorszky]

As everything travels upwards, the 7 and 9 also travel upwards, but they're only feature once in 40 each, because they're at the edge. The star features twice (once in blank, once in heart), so we get 40 = 7 + 9 + 2 star, or 24 = 2star, or 12 = star, and from there sub star back, which gives up 21 = heart, and then 21 + 12 = 33 for star + heart.

[@RAFAELSILVA-by6dy]

If you were really stuck, you could start with star = 1, which is too low, and increase star until star = 12 solves the triangle. What I've noticed when helping people with maths is how reluctant students are just to try things to see what happens. Also, doing this basic process reveals how the triangle works - every time you add 1 to star, you add 2 to the apex. Then, you can work out for yourself that 40 = (7+star) + (star + 9) - even if you didn't see that immediately.

[@redpacific359]

Now i will rewrite the heart shape is a, star is b and the empty cell as c. so we have b+9=a, b+7=c, a+c=40 so that means 2b+9+7=40 -> b=(40-9-7)/2=24/2=12 then we can see a=21 and c=19 we found a,b,c so we can calculate a+b=21+12=33. isn't it easy for adults?

[@S8EdgyVA]

It took me a moment but once I sat down and filled in the gap, I realized that the actual equation is rather simple. You see, since we need to add the two numbers below to get the number up top, the empty square had the value 7+⭐, and therefore the 40 was 7+🌟+❤... (because we're looking for ⭐+❤, I'm gonna replace it with an x) so our equation is x+7=40, which you might remember from basic algebra. The answer is 33

[@labadf]

Another approach could be that the numbers on the middle row are going to be always with a difference of 2. Then we can ask what two numbers, with a difference of 2 between them, add up to 40? Divide 40 by two, and add and subtract 1 to each side. The answer gives you "heart" and "blank". Having those, you can easily get "star". But I liked your third approach more.

[@iamrandomnesshumanoid9321]

I also had a gut feeling idea, so I tested it with the first pyramid. I added all the bottom numbers, 2+4+3, getting 9. 9 is 4 less than the top number, 13. The middle number on the bottom row was that difference. Then I applied the same logic to the unknown pyramid. 7+star+9=40-star, meaning 2star=24, making star 12. Then I do the simple addition of 12 and 9 to find heart, 21. Add star, 12, and heart, 21, and I get my solituon of 33. It was a fun challenge and I was glad it worked. Very fun to see the other ways to come at this problem though.

[@StarScapesOG]

I went: top number is equal to the first number on the bottom row plus two times the middle number plus the last number. So, for the actual problem: 40=7+2☆+9 subtract seven and nine from both sides and divide both sides by two, and you get 12. Then ♡=12+9=21. So ☆+♡=12+21=33. Not as elegant as your first and third solutions, but it did work (if any of what I typed is even coherent...)

[@gamer122333444455555]

Many don't know how or won't put forth the effort to make an equation out of a diagram or word problem. Unfortunately, a visual representation is not always a useful example even if it is clear.

[@theboneidentity]

Adding all adjacent numbers at the base is equal to the top, solving that equation gets your first variable, the ⭐: (7+⭐)+(⭐+9)=40 would make ⭐=12. From ther, you then get value of ♥= ⭐+9 = 12+9 = 21 Then the Blank=7+⭐=7+12=19 2nd row, where blank + ♥= 19+21 = 40. ⭐= 12 ♥ = 21 Blank = 19 No need to guess.

[@jessicaolson490]

0:31 *=12,

[@TheKasperHermans]

My method is different. The difference between 9 and 7 is 2. So the difference between blank and heart is 2 either. Since the same amount is added. 40/2 = 20. Add one for heart (21), minus for blank (19). 21-9=12=star.

[@magnetospin]

My approach was that the top number=bottom side numbers + 2 times bottom middle number, so 40=7+9+2*, which can be easily solved and gives us *=12, the rest is straight forward.

[@Vidchemy]

In the first triangle, a number is equal to the two adjacent numbers in the row below, or 13=6+7, 6=2+4, and 7=4+3. With substitutions from the bottom row, you can also get 13=(2+4)+7 or 13=6+(4+3). Now, make analogous equations for the second triangle, disregarding any that would include the blank position. This results in 40=7+☆+♡ and ♡=☆+9. Next, substitute ♡ and solve for ☆. This gives 40=7+☆+(☆+9), which reduces to 40-(7+9)=2☆, or ☆=12. Finally, ♡=12+9=21.

[@weignerg]

Another pattern to notice is that the triangle's numbers are approximately 3 times the size as the other one. Taking 7 and multiplying by 3 gets 21 7*3=21 Then 21-9=12 21+12=33 ☆ + ♡ = 33

[@todd3143]

33? yay. but the way i solved it was using stuff i learned in middle school, so… this was kinda mean for children

[@kenmore01]

The mid-left box is as vacant as the person's brain who made up this problem.

[@disraelidemon]

The middle number on the bottom row is added to each of the outer numbers, to make the two numbers on the middle row, which are added to make the number on the top row. So the two products of the bottom row additions must add up to 40. Since there's a difference of two between the outer numbers on the bottom row, there must be a difference of two between the numbers in the middle row, which must add up to 40. So the middle row numbers must be 19 and 21, and by subtraction, the central bottom row number must be 12. So the values for the two symbols are 12 and 21

[@anonymous.3458]

Simplest solution I can think up is dividing the top number by two, then finding the difference between.the two bottom numbers, as the difference betweem 7 and 9 is equal to the difference between x and heart. You then divide the difference by two, subtract from the side with the lower value and add to the side with the higher value. Then you simply subtract 7 from x, and 9 from heart, both giving you the solution to star and giving you a method of checking the previous step. Basically just x=7+star, heart=9+star, heart-x=9+star-(7+star); heart-x=9+star-star-7; heart-x=9-7; heart-x=2. Heart+x=40; Heart=(40/2)+2/2; (since adding one to a side neceasarily subtracts one from the other.); Heart=20+1; Heart=21; 21+x=40; X=40-21; X=19; Star=x-7; Star=19-7; Star=12; Star=Heart-9; Star=21-9; Star=12; 12=12, therefore, the answers for x and heart are right. Then simply heart+star=21+12; Heart+star=33. (And yes the equations were both a pain, and fully unnecessary, as the whole point was to base it off of the relationship within the setup. However, 1. I'm a perfectionist, and 2. I honestly wasn't sure I could break this down into an actual equation, which made me want to even more.)

[@Mr107828]

My approach was to see that 13-(2+3)=8. Since we add the number in the middle of the bottom row to both corners individually, it means we get this number twice. That leaves us to divide 8 by a factor of 2 to get 4. This was the example pyramid. Now we apply the same trick to our challenge pyramid. 40-(7+9)=24. We now know to divide by 2, so 24/2=12. So star=12. Add 9+12=21. And finally add 21+12=33. It took me about 5 seconds to come up with this trick.

[@Prypak]

You know the "star box" will be counted twice, while the corner boxes will be counted once, so you have 2stars=40-7-9 2stars = 24 star = 12, therefore heart = 21. More comprehensively, you can start with the top and name box next to heart = 40-heart. And write a system (with heart = star+9)

[@andreasarnoalthofsobottka2928]

Three equations three unknowns. This should not baffle adults.

[@stevenleonmusic]

It's not terribly difficult to just solve for all three variables, Heart, Star and Blank, using substitution: H = 9 + S B = 7 + S B + H = 40 --- (7 + S) + (9 + S) = 40 2S + 16 = 40 2S = 24 S = 12 --- H = 9 + 12 H = 21 B = 7 + 12 B = 19 --- 21 + 19 = 40 Star = 12, Heart = 21, Blank = 19 That seems more useful to me...

[@josgalgebra3784]

A possible way to solve with two simple equations, two variables. Use something, ,,.... h for the heart shape, and x for the star shape. See that the space in middle row is 40-h. Then the rule for this pyramid puzzle becomes set of equations 7+x=40-h and x+9=h. This should be very easy to solve. I am finding h=21 and x=12.

[@elliottwade1901]

As the ostensible "parent" in this situation my sense was to use algebra, but the least amount of it possible: x + y = 40 7 + z = x z + 9 = y substitute to obtain expression for z --> 7 + z + z + 9 = 40 2z + 16 = 40 2z = 24 z = 12 substitute z = 12 into the pyramid and solve by inspection: 40 x=7+12 y=12+9 7 12 9 --> y + z = 33

[@soaringvulture]

Yeah but when I was 9 I didn't know algebra and would probably have been baffled by this problem.

[@zae0616]

The middle row is comprised of two sums, left plus middle and right plus middle. So the 2nd row is left + 2 x middle + right. Since the 2nd row adds up to the top row, 40 = 7 + 9 + 2X, so (40 - 16) / 2 = 24/2 = 12, so X aka star = 12, that makes "heart" = 12 + 9 = 21. So 12 + 21 = 33 is start plus heart. Pretty much the same as @llaffer.

[@MultiMusicMan]

I saw the thumbnail, didn’t expect to solve it, then solved it without the video in 30 seconds, and thought I’d see why an adult was baffled by an arguably simple problem.

[@lordd007]

Left pyramid: 13 - 2 = 11 which is the same as adding 7 from mid and the 4 below. Following the same pattern, 40 - 7 = ❤+⭐️= 33

[@Randomturtle001]

Personally I found that the number in the bottom middle is used twice to make the number at the top, and the outside numbers used once. So I subtract 7 and 9 from 40 to get to 24, then divide that by 2 and then have 12 in the bottom middle. From there we can work out the 2 numbers above it by simple addition. getting 19 and 21. We can check that 19 and 21 add up to 40, so we know all numbers are correct. Then we can add 12 and 21 for the answer of 33.

[@davidbergeron78]

The top number, 40, is always equal to the 7 + 2 x star + 9. So star is 12. Top always equals bottom left plus right plus 2 time middle number.

[@bbdnn4249]

One only needs the numbers in the top of the triangle and bottom left of the triangle to solve this. The number in the bottom right of the triangle is not necessary. Any other number could be substituted for the bottom right number and the result will still be the same when adding up the middle bottom number and right middle number.