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Child's homework puzzle is baffling adults

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Can you solve this number pyramid puzzle?
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5 сен 2024

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Комментарии : 900

@edmx Месяц назад

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

@Patrik6920 Месяц назад

Lmao 😂

@calholli Месяц назад

Women.. 🍵

@timothyvenable3336 Месяц назад

Haha so true

@mickdavies5647 Месяц назад

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

@ambhaiji Месяц назад

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

@llaffer Месяц назад

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 Месяц назад

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 Месяц назад

This was my approach as well.

@anim8edpatrtiots803 Месяц назад

Same instinct here

@_ZAOB_ Месяц назад

Me too

@gristor Месяц назад

Same here :)

@JonSebastianF Месяц назад

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

@seanh884 17 дней назад

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

@ne9958 10 дней назад

@michaeledwards2251 10 дней назад

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 8 дней назад

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 6 дней назад

@@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.

@CharlesBallowe Месяц назад

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.

@Ldogflp Месяц назад

Yeah I did the same thing

@colors6692 Месяц назад

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

@CharlesBallowe Месяц назад

@@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 Месяц назад

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

@neilgerace355 Месяц назад

@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.

@xyzct Месяц назад

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 12 дней назад

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 11 дней назад

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 10 дней назад

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

@joepiazza3756 9 дней назад

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 6 дней назад

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

@NerdByAnyOtherName Месяц назад

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 Месяц назад

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

@myyoutubeid5451 Месяц назад

Ywp this is simple way, no algebra required

@EnriqueAThieleSolivan Месяц назад

True. Only sum, and subtraction are needed.

@giantchook3368 8 дней назад

That’s how I did it.

@craigising День назад

This is also how I achieved 33.

@dumptrucc2458 Месяц назад

Easiest MYD problem by far

@andrewhooper7603 Месяц назад

don't take this w from me

@petasmith6258 Месяц назад

I agree, got it straight away 😮

@Boostthenoob Месяц назад

True, I did it in my mind easily

@chazbo2672 Месяц назад

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 Месяц назад

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

@quantumgaming7643 Месяц назад

this one is quite easy ngl

@NabeelFarooqui Месяц назад

It's for 9 year olds

@doge9737 Месяц назад

@@NabeelFarooqui lmao

@lukasjetu9776 Месяц назад

true, solved it in around 30 secs

@wasikancb Месяц назад

Solved it in my head before clicking on the video

@lukasjetu9776 Месяц назад

@@wasikancb same

@verkuilb Месяц назад

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.

@TravisGn02 Месяц назад

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 Месяц назад

@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 Месяц назад

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

@gswcooper7162 Месяц назад

@@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 Месяц назад

@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 Месяц назад

@@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

@davidreid7293 Месяц назад

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

@florianmoosbrugger5177 Месяц назад

This was also my first idea...

@spitalhelles3380 Месяц назад

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

@R0bot4 Месяц назад

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

@whlee9382 Месяц назад

@@spitalhelles3380holy that’s hard

@2righthands816 Месяц назад

@@spitalhelles3380 129, ez!

@HolySoliDeoGloria 25 дней назад

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

@michaelsorensen7567 9 дней назад

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

@AndRooooooo 6 дней назад

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

@dontworrybehappy5139 Месяц назад

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 Месяц назад

That's exactly my solution.

@thunderatigervideo Месяц назад

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.

@ErikBongers Месяц назад

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.

@wobaguk Месяц назад

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 Месяц назад

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.

@niroshanaperera7330 Месяц назад

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 Месяц назад

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

@TheAstronomyDude Месяц назад

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

@rayraythebrew2863 Месяц назад

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

@jwbjerk 3 дня назад

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

@johncrwarner Месяц назад

if you call the three base numbers a, b, c then the next layer is a + b and b+c so the top layer is a+2b+c The sum require (heart plus star) is b plus b+c giving 2b+c so top number (a+2b+c) minus bottom left a always equals 2b+c

@kingsonicxx Месяц назад

Simple... 7+* is the free shape, *+9=❤ so we can switch them out 7+*+*+9 = 7+9+2* and this is 40 So 16+2*=40, 2*=24 so *=12 And to prove: 7+12=19 for empty, 12+9=21 for ❤ 21+19=40 And sum that up you get *+❤=12+21=33

@MB-ny6is Месяц назад

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

@cmuller1441 Месяц назад

Seriously? 7+🌟=⬜ ⬜+❤=40 So 7+🌟+❤=40 🌟+❤=33 Longer solution: 7+2x🌟+9=40 (top=sum of bottom with 2x for middle element) 🌟=12 ❤=9+🌟=21 So: 🌟+❤=33

@lux5164 Месяц назад

this video did not need to be 8 minutes long

@ashishkadakia1129 24 дня назад

Lot of problems are like that. You don't need to do whole math or solve all the variables in order to find their sum or value that we are looking for. We need to investigate and trust other methods as well. It's also called talent.

@jackychanmaths Месяц назад

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

@ian1231100 8 часов назад

Did this before watching the video. My logic is that the number is the sum of the two numbers under it, which makes ❤=⭐+9, and the blank space 7+⭐. Based on this logic, we can come up with this equation: (7+⭐)+(⭐+9)=40 7+2⭐+9=40 16+2⭐=40 2⭐=24 ⭐=12 Now that we find ⭐, we can use it to find ❤. ❤=⭐+9 ❤=12+9 ❤=21 Therefore, ⭐+❤ =12+21 =33

@huzefa6421 Месяц назад

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 Месяц назад

Same

@shooshyw4509 3 дня назад

I once saw a video when it said 2 seconds ago

@clairecelestin8437 Месяц назад

I noticed that pascal's triangle gives the coefficient of how many times a given block of the pyramid will contribute to the sum at the top, so 40 = 7 + 9 + 2(star)

@TheKsh Месяц назад

I didn't watch the video but i did it like this. 2 + 3 + (4*2) = 13 By the same logic. 7 + 9 + (⭐*2)=40 ⭐= 12 ❤= 21 [12+9]

@labwax Месяц назад

Used the same logic 🙂

@clemente3966 Месяц назад

I think you meant 3 instead of that 5 in the first equation

@TheKsh Месяц назад

@@clemente3966 yes, thank you

@crusherskyy Месяц назад

spent the first half of the year learning dynamics and it really helped solve this

@RJFlute Месяц назад

I'm baffled by where the confusion was.

@milanstevic8424 Месяц назад

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 Месяц назад

@@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 Месяц назад

@@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 Месяц назад

@@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 Месяц назад

@@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.

@Maninawig Месяц назад

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

@Georgggg Месяц назад

(7+✡)+❤ = 40 ✡+❤ = 40 - 7 = 33

@otakurocklee Месяц назад

exactly. The 9 is completely irrelevant to the problem.

@jimi02468 Месяц назад

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

@AndrewBlucher Месяц назад

Wrong ⭐

@craigsaunders7037 Месяц назад

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

@AndrewBlucher Месяц назад

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

@alexanderkuhn1335 Месяц назад

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.

@joemyk Месяц назад

Star = 12 Heart = 21 Edit: Sum = 33

@otakurocklee Месяц назад

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

@guypanton8341 Месяц назад

I like your solution, but. Clean.

@engi_games 2 дня назад

That’s, not how algebra works

@guypanton8341 2 дня назад

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

@frisbo90 Месяц назад

Fascinating how the sum heart + star = 33 is not depending on 9. They can put other values different from 9, heart and star will have different values but their sum will remain equal to 33

@priyank5161 Месяц назад

Isn't it obvious? All that matters is the value of star, u see, if u change the value from 9 to any other value, the value of star would change accordingly, i.e, star is dependent on 9 itself, For example, if it was 10, then the heart must be, star + 10... And, the blank area should be star + 7, but we need to find 2 x star + 10 Or in a general solution where the heart is h, star is s, and the value 9 as a variable can be termed as x and blank area be b We get our h = s+x, and b = s+7 We need to find s+h, or, 2s + x, but we also know 40 = 2s+x+7 And hence 2s+x = 33 No matter whats the value of x is, it will always be 33

@davidjessop2156 Месяц назад

Way too long for a trivial problem

@stigmontgomery7901 10 дней назад

Maybe because MYD was exploring other solutions?

@davidjessop2156 10 дней назад

@@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.

@mittfh Месяц назад

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 Месяц назад

I just brute forced it lol

@romain.guillaume Месяц назад

33. My reasoning : following the rules the 40 in the top row is the sum of the sides and twice the sum of the middle of the base. Thus 7 + 9 + 2 stars = 40 star = 12 Besides, heart = star + 9 Thus star + heart = 2*12 + 9 = 33

@KiloOscarZulu Месяц назад

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 Месяц назад

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 Месяц назад

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.

@hayn10 Месяц назад

write as 7+x+9+x=40 x will represent the star simplify 16+2x=40 subtract 16 2x=24 divide by 2 x=12 the heart is 9 more than the star, so we have 12+21=33

@eds1942 Месяц назад

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 Месяц назад

why tho?

@eds1942 Месяц назад

@@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 Месяц назад

@@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 Месяц назад

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 Месяц назад

@@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.

@TheWealthBuildingJourney 5 дней назад

0:58 Doing this logically, make the middle row both 20 for the blank and 20 for the heart. Working backwards, again sub in 13 for the star. Now, adding 9 and 13 gets to 22, so the number for the star is too high. Take the difference of the two sides in the middle row (blank is 20, heart is 22, difference is 2) and divide it by 2 (2 ÷ 2 = 1) and reduce the star by this amount (13 - 1 = 12). The correct answers are star = 12, heart = 21, blank = 19, and the final problem: ☆ + ♡ = 33. I thought of another way to solve it: 7 + 9 + 2×☆ = 40, 40 - 16 = 2×☆, 24 = 2×☆, 12 = ☆. The middle row numbers must equal the top number and the middle number in the bottom row is common to both solutions (7 + ☆ and ☆ + 9). Since these two intermediate numbers (blank and heart) must equal to 40, this shortcuts the iterative work: set the bottom row equal to the top row and solve the basic algebraic equation.

@lexnellis4869 Месяц назад

I did the guess and check. Started by making ☆=11, found X+♡=38. Made ☆=13 and found X+♡=42. Took ☆=12 making X+♡=40 then just added ♡+☆. Brute force, sure, but still only 3 tries. Clearly, your math training shows better reasoning.

@Vidchemy 11 дней назад

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.

@cyn4476 9 дней назад

the two bottom numbers are two apart, so we can assume the two middle numbers will be two apart. The only option that adds up to 40 is 19 and 21. Star is 12, answer is 12 + 21 = 33.

@Dr_piFrog Месяц назад

Blank box = n, then n = 7 + star => 40 = 7 + star + heart solving for (star + heart) = 40 - 7 = 33 which give the required answer. Completing the solution of Pyramid: Pyramid: top ,, bottom star + heart = 33 star = 12 and heart = 21

@redpacific359 Месяц назад

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?

@bkm83442 Месяц назад

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.

@marcfruchtman9473 Месяц назад

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.

@Rotom2304 Месяц назад

It's like Serpinski's triangle but upside down. 2+4=6, 4+3=7, and 6+7=13. So, in the other triangle, 7+star=black and black+heart=40. Substitute in and 7+star+heart=40. Subtract 7 from both sides and star+heart=33 The fact that star+9=heart is irrelevant to solving the puzzle, but we can use it to figure out what the unknowns are anyway. Star+star+9=33 2star=24 Star=12 7+12=black 19=black 12+9=heart 21=heart And to check work, 21+19=40 All good.

@Rotom2304 Месяц назад

Oops, I meant Pascal's triangle.

@collingallaway5541 Месяц назад

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

@MarieAnne. 28 дней назад

My thought: blank space in pyramid = 7 + ★ Therefore, top row is (7 + ★) + ● = 7 + (★ + ●) But top row = 40 = 7 + 33 = 7 + (★ + ●) Therefore ★ + ● = 33 So we don't really need 9 to solve this specific problem, but we do need 9 if we want to solve the rest of the pyramid.

@bloodboughtsaint777 10 дней назад

I saw the thumbnail and thought, "This will be fun! I may have to use a system of equations to solve this!" I always start these by writing the problem down (in this case, copying both triangles and their respective values). I quickly realized that I could just derive the value at the top of the triangle with the values at the bottom. I then wrote my quick proof just to be sure, and it did work out that way. (2+4) + (4+3) = 13 ... Simplified to 2+2(4)+3 = 13... so then I simply wrote out 2*+16 = 40, and it was all downhill from there.

@rndmevil 8 дней назад

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.

@weignerg 27 дней назад

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

@BleuSquid Месяц назад

With a being the top, b and c being the middle, and d, e, and f the bottom row. a = b + c b = d + e c = e + f Therefore, a = d + e + e + f = d + 2e + f a - d - f = 2e e = (a - d - f)/2. a, d, and f are given: e = (40 - 7 - 9) / 2 = 12 Now we know e (star) and f, we can find c (heart). c = e + f = 9 + 12 = 21 e (star) + c (heart) = 12 + 21 = 33

@Dillsfawn 7 дней назад

This was my solution: Bottom right corners of each triangle is 3 and 9. 3 is one third of 9. Since the triangles are the same proportions, each number in the left triangle is one third of the number in the matching position of the right triangle. 7 matches heart, 7 * 3 = 21 4 matches star, 4 * 3 = 12 21 + 12 = 33

@angeldude101 Месяц назад

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.

@FingerswithStyleAcoustic Месяц назад

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!!!!!!!!!

@elliottwade1901 Месяц назад

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 11 часов назад

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

@Mr107828 Месяц назад

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.

@AspieGamer13 Месяц назад

Your way to approach at the beginning is exactly how I thought to solve it as well: looking for a pattern in the other triangle. I then did guess and check to verify (starting at 8, then 10, then 12)… mostly because I was solving this in my head while I’m watching on TV and only have my phone available (used for this comment)

@Prypak Месяц назад

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)

@warny1978 Месяц назад

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.

@brunocamposquenaoeoyoutuber 12 дней назад

Here is how I did it after you gave the "trial and error" approach: I tried 2, but it was 20. So, since the middle row gets multiplied by 2, I tried 12, which would mean the middle row is 19 and 21, and the sum of that is 40. So, 12+21 would be 33, which fits your initial assumption.

@proffessorclueless Месяц назад

Labelling each box from left to right from top to bottom a to f inclusive, we get the following rule set Rule 1 a=b+c Rule 2 b=d+e Rule 3 c=e+f. Substituting rule 2 into rule 1 we get a=c+d+e then deduct d from both sides we get a-d=c+e. Therefore heart (c) + star (e) = a(40) - d(7) = 33.

@aliquida7132 Месяц назад

I really have a problem with the blank. Not sure why it bugs me so much, but there should be a symbol there to indicate that there should be a value there... rather than nothing at all.

@milanstevic8424 Месяц назад

I'm getting you have a big problem with the crosswords or sudokus as well.

@aliquida7132 Месяц назад

@@milanstevic8424 Not at all, it is a matter of consistency. For this one, there are three unknown values, two have symbols and one is null. For crosswords and sudokus, all unknowns are null.

@zenaku666 Месяц назад

I'm actually genuinely curious why? Why can't a blank box be a variable box? Why must it have a label? And why can't you label it yourself?

@aliquida7132 Месяц назад

@@zenaku666 If all variables are blank boxes, then a blank box is a variable. If all variables are a label, then a label is a variable. If there are known values, and blank boxes and labels... then the rules aren't consistently applied. In many puzzles that have variables and known values, any additional "blank" spaces are blank because they aren't part of the puzzle at all. But this blank value is part of the puzzle. The blank would be "nothing", not even zero, nothing, because it isn't part of the puzzle. But that can't be the case here, otherwise "nothing" plus heart would equal 40.

@zenaku666 Месяц назад

@@aliquida7132that's an interesting way to look at it I suppose. But I don't think I follow. I'm not sure what puzzles you are referring to but there are several puzzles where blanks are meant to be filled using context clues from the rest of the puzzle: sudoku, crossword puzzles, fill in the blanks etc. in these puzzles the point is to fill in the blanks. Why isn't this one of those instances? In the instances you're thinking of aren't the blanks shaded or otherwise crossed out to indicate they can be safely ignored? If we assume ❤️ is 40 doesn't that imply the blank box is 0? The rule as established by the first triangle is cells are the sums of the ones below it, except the cells in the bottom row. Is this not the rule?

@SanchiVerma Месяц назад

You just have to make 3 equations Let star= x, blank =y and heart =z Now, 7 + x =y and 9 + x =z And y+z = 40 Substituting the value of y and z, We get: 16 +2x = 40 Therefore x =12 and a = 21 ⭐ + ❤ =33

@Richie_P 11 дней назад

First thing I noticed was that x is ⭐+7 and 🤍is ⭐+9. Therefore, 🤍is 2 larger than x. The two numbers that add up to 40, and are 2 apart, are 19 and 21, which makes 🤍=21. That means⭐=21-9 =12. And, of course, 12+21=33.

@ScottM1973 Месяц назад

Started with observation that Top = Sum of Middle = Sum of factors of numbers on Bottom So 40 = ? + ❤ = (7 + ⭐) + (⭐ + 9) Therefore 40 = 7 + 2⭐ + 9 2⭐ = 40 - 7 - 9 = 24 Making ⭐ = 12 ❤ = ⭐ + 9 = 12 + 9 = 21 Finally ❤ + ⭐ = 12 + 21 = 33

@RoderickEtheria 10 дней назад

Star=12, Heart=21. The total of the top number is divided into two middle numbers, which both get divided into the numbers into each one of them. Both middle numbers share the middle bottom number. 40-7-9=24/2=12. 12+9=21. 12+21=33.

@Knaagobert Месяц назад

A: star + 9 = heart B: heart + 7 + star = 40 insert A into B: (star + 9) + 7 + star = 40 --> 2 star = 24 --> star = 12 --> insert in A: 12 + 9 = heart = 21

@ApolloArcher1 15 дней назад

After knowing the answer, I came up with another solution (I haven’t watched the video yet, I only looked at the thumbnail). Based on the evidence we have, we know that the middle tier has to equal 40 when combined right? But what are the numbers? That’s simple. The left has to at least be 8 and the right has to at least be 10 because it’s adding the bottom numbers to each side that they are connected to. If you start with 1 as the star then the middle layer will combine to be 18 which won’t be enough to reach 40, however you do now know which number the star is meant to be though. By starting with 1 as the star and getting 18 as the result, you find that you are missing 22 from the total. As you add two sides together to make 40, you thus split the 22, getting 11, which you add to the star and from there you combine the numbers again to get 40. This was something I did in about 5 seconds in my head, but explaining it in words makes it more confusing and much longer. Though I hope this perspective might help someone who see’s this in the future

@RAFAELSILVA-by6dy 14 дней назад

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.

@shrankai7285 Месяц назад

My immediate thought was that the top was the bottom corners plus twice the middle bottom number. Simple algebra from there giving the bottom to be 12, and the middle right to be 21. 12+21=33

@foogod4237 7 дней назад

There is a slightly more sophisticated version of "trial and error", which actually turns out to be a well established mathematical technique: *Successive approximation.* In your "guess and check" example, we start as before by choosing, say, 1, and it ends up with 18 at the top instead of 40 (as you showed): *(star)=1:* 7 + 1 = 8; 1 + 9 = 10; 8 + 10 = 18 _(too low!)_ But _how far off_ is our answer from what we want? Well, 40 - 18 = 22, so we need 22 more than what we have. Let's try just adding that to the value of (star) for our next guess and see what happens: *(star)=23:* 7 + 23 = 30; 23 + 9 = 32; 30 + 32 = 62 _(too high!)_ Now we're too big. By how much? Well, 62 - 40 = 22 (the same amount in the other direction. How curious!) So, logically, the answer we're looking for should be somewhere _halfway between_ 1 and 23. Exactly halfway between 1 and 23 is 12, so let's try that: *(star)=12:* 7 + 12 = 19; 12 + 9 = 21; 19 + 21 = 40. *bingo.* (and it only took three guesses!) Then, of course, solve from there as described in the video. Actually, ironically, if you chose to start off with a more conservative approach to the approximation, and add or subtract _half_ of the difference by default, then you'd actually hit it spot on on only your _second_ guess. (Personally, though, when I did it, I just realized that the top space is going to be equal to the bottom left + 2 times the center + the bottom right, so 40 = 7 + 2(star) + 9, so 2(star) = 24, and (star) = 12. From there, it's easy to calculate heart, and then the answer.)

@AzureKyle Месяц назад

From the look of it, to me at least, the pattern seems to be two numbers on the bottom row, add up to be the number above them. So in the given triangle, we have 2+4=6, 4+3=7, and 6+7=13 So from that logic, we have 7+Star=Blank, Star+9=Heart, and Blank+Heart=40. You can also deduce that the bottom row, with 2* the middle number, all add up to the top number. 2+4+4+3=13, and 7+Star+Star+9=40. With this, we can subtract 7 and 9 from both sides to get that 2Star=24 Divide both sides by 2, and you get Star=12. So now we plug that into Star+9=Heart, to get 12+9=Heart, and can figure out that Heart=21. And so Star+Heart=12+21=33. Also, while not needed for the answer, we can also deduce that Blank=19, because 7+12=19, and can confirm this with Blank+Heart=19+21=40

@AtriasNaradan 8 часов назад

Back in the 90s, this kind of math problem that requires the understanding of the theory of equations, was middle-school level for 13-15 years old...not for 9 years old lol Anyway, your trial and error way is taking too long, trying from 1, 2, and so on for the star symbol. It's faster to use the logical understanding that 40 : 2 = 20, and start from that. If we do that, we can quickly see that 20 is not possible for x and heart, because the bottom numbers are 7 and 9, and then we will also see that star can't be lower than 10, because x and heart can't both be below 20. So, from there, we can start the trial and error by the logical assumption that the symbol star ≥ 11. While this step looks longer being explained like this, in practice it will be way faster trial and error than starting from star = 1 👍

@bjornbero Месяц назад

From the explanation tower: 2+(2x4)+3=13, bc 13=6+7, so 13=(2+4)+(4+3), with this in mind 40=7+(2x⭐)+9, 24=2⭐, ⭐=12. ⭐+9=🖤, 12+9=🖤, 🖤=21 ⭐+🖤=12+21=33 Or: since 7 and 9 are 2 apart, 🖤 and 'blank' also need to be 2 apart, so that means 'blank'=19 and 🖤=21 🖤=7+⭐, 21=7+⭐, ⭐=12

@tncookies 5 дней назад

You can add the 7 and the 9, then say how many more to get to the top? That would be 40 -- (7+9) which is 24. You'd divide that by 2 to get star, because you'd have to add star twice to get to the top, once to the 7 and once to the 9. Then you just add the 9 and the 12 to get heart, which would be 21. So star plus heart = 12 + 21, which equals 33.

@zwei-p1993 Месяц назад

My solution was to first assume both blocks on the second floor were 20. Then I took the average of 7 and 9, which is 8, and subtract it to both numbers, 7 and 9 → -1 and +1. Apply them to the blocks on 2nd floor, as they become 19 and 21 (heart). Subtract one of them with the already given number below, reveals the star to be 12. Finally, add heart to it and the result is 33.

@tanelkagan Месяц назад

My method was to note the difference between 7 and 9 i.e. 2, and reason that (7 + ⭐️) must be 2 less than (9 + ⭐️). In turn, that means that 40 is the sum of two numbers, one of which is 2 greater than the other i.e. 19 and 21. The greater of these (21) must be on the 9 side, so 🤍 = 21. As per the rules set out, 🤍 is the sum of the two numbers below it i.e. (9 + ⭐️) = 21, so ⭐️ = 12. Therefore 🤍+⭐️ = 21+12 = 33. Ultimately all the methods rely on the same algebraic relationships, it's just a matter of presentation and the order in which those relationships are looked at.

@drummerrck Месяц назад

Start at 20+20 in the middle row and work in opposite directions along the number line.

@marlupus801 Месяц назад

My first reaction was "top box is equal to bottom left plus bottom right plus (bottom middle X 2)". I was able to solve the whole triangle from there and got the final answer.

@easy_s3351 Месяц назад

Blank (B)+Heart (H)=40. B=7+Star (S), H=9+S. So 7+S+9+S=40 gives 2S=24 so S=12. That means H=9+12=21 and therefore H+S=21+12=33.

@manudude02 Месяц назад

Row 2 will have an average of 20, right will be left+2 so it will be (19,21), then subtract 9 from 21 to get 12. Finally 12+21=33

@timothyfaust4606 Месяц назад

There is a much easier way to do this without guessing and checking. Because the middle number is used in two factors. You could write this as 7+2*⭐+9=40

@AutisticAnn Месяц назад

I looked at the numbers on the bottom, let’s say a, b, and c, and noticed we were adding a+b=d and b+c=e, and d+e=f. So that means (a+b)+(b+c)=f, and a+b+b+c=f, a+2b+c=f, and plugged in 7+2b+9=40. 40-9=31. 31-7=24. 24/2=b=12. 12+9=21. 21=e. 12=b. We want b+e. 21+12=33. Ez.

@tom.1 Месяц назад

The difference between the numbers in the middle row has to be 2 since the difference between the outer numbers in the lower row is 2. Therefore the numbers in the second row can only be 19 and 21 (heart). Star = 21 - 9 = 12. Star + heart = 33.

@theboneidentity 8 дней назад

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.

@shawnheidingsfelder8179 Месяц назад

I made an equation for the star, the heart, and the blank space, which I called A, B, and C. The heart equation I put in terms of A, plugged that into my equation for the blank space (C), and subbed that equation for C into my equation for what added up to 40, so B was my only variable. Solved for B, then plugged that back into the other equations to find A and C, then answered the question asked. C wasn't totally necessary (the blank space in the pyramid), but knowing it helps check your answers.

@Complexitor37 Месяц назад

This took me about 30 seconds to figure out how to solve. Write all the equations down and you have an easy system of equations. Star=x heart=y blank=z. z+y=40. Both z and y are just x added to a known number. Substitute and you get (x+7)+(x+9)=40, which is easy algebra.

@cparks1000000 Месяц назад

You don't need to come up with guess here at all. The only relationship in the puzzle that involves ♥ is 🍊 + ♥ = 40 where 🍊 is the blank space. It's then true that 7 + 🌟 = 🍊. Putting everything together gives 7 + 🌟 + ♥ = 40.

@SwedeRacerDC 10 дней назад

This is child's play. Quite literally. I solved the entire puzzle. 40 is equal to the sum of the two unknown variables below it, which each equal the sum of the two numbers below them. This includes 7 and 9, as well as two times ⭐ because the star will be included in both sides of the middle. Simplify that equation and you will get your answer for what each variable is and then you can add the two together. It's a nice little trick and I kinda noticed the pattern on the right, but didn't think about comparing it to the left to make sure it's a pattern.