Math Problem That Went Viral in 2020. Can you solve it?

This math problem is the meaning of life. Can you solve it in less than 30 seconds?

You will have to use geometry and all the information on the diagram - and like all good matht problems on Youtube I will go through how to work out the answer.

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[NextWaveTracks]

I solved this with using a faster method after pausing the video.

First just add the diagonal segments together (48 + 24) = 72.
So the answer is (72 - 30) = 42

Moving the center point around always makes one quarter smaller while the other gets larger. The total area of the square never changes.

[umbraemilitos]

For any square, partitioned from midpoints of the sides to a common interior point, the sum of diagonal areas must be equal.
(48+24)-30=42

[Baerchenization]

I wanted to solve it in 5 seconds, slightly unscientific, but since this is obviously a construed, easy problem:


1) it starts with the assumption that the area is square (and already expecting a round number, as the 3 known areas are).
2) I add the 3 known areas = 102
3) the missing area is about same size as bottom right...
4) so we are looking for a square that is lacking ca 40 or so cm2 - coming from 102 that will be 144 (12x12), because 169 (13x13) would already be way too large and 121 is too small. So since we already have 102, the area we are looking for is 42 (144-102). There you go :)

[avinashmreddy]

It's very simple. It's a square so total area must be a perfect square. 24+30+48 is 102. Closest perfect squares after 102 are 121 and 144. 121 is not possible as the shaded area is almost as big as the area to the right of it. So it has to be 144. So now 144-102=42 😊

[zerosumgame]

Also a cool way to show that the two diagonally opposite sections will always be half the square when split up like this. So next time you will know that 24 + 48 must be half the area.

[manaphylv]

You can also solve this by logic and intuition. Simply look for square numbers that "fit, " and you'll quickly find that 144 (12²) is the only logical guess, because the lack of decimals suggests that the side length is an even number, and 100 (10²) is too small while 196 (14²) is too big.

[WhatB]

Thank you Techmath for the exercise. Thank you to the commentors for your detailed explanations of your solutions. I wasn't able to hear the intended explanation due to a volume issue so, thankful for the community for your share.

[cloroxbleach]

I just thought (and hoped lol) of the answer as a whole number (no decimals) and since it's a square, the total area must be a square as well. If you add the given areas it gives you 102 (24+30+48).The next biggest square is 121 but that would mean the area of the shaded region is 19 which is logically impossible since its too small, so it had to be 144 hence area shaded = 42.

[cyancoyote]

For some reason my intuition instantly told me to do the equation [24+48 = 30+x], solving for x gave me 42, then I checked whether or not the sum is a square number. It was, so I concluded that I was correct. Nice exercise.

[caijp]

I found the difference between 24cm2 box and 30cm2 box =6 cm. so I applied the same to the 48cm2 box 😂 I just so happened to get the right Answer.

[novasprint]

Please someone correct me if the method I used is wrong.

I thought that since the area of the 4 parts are not decimal number the side length could only be an integer. So with that logic I added the area of the 4 parts together and substract it by the nearest square number. So by adding the areas you 102 and the nearest square is 121, which means the side length is 11. By substracting the whole area of the square by the known areas you get the unknown area which here is 19. Sinc you can see the unknown area is clearly bigger than 19, so I added one to the side lenght. 12 squared is 144, 144 minus 102 is 42 and thats how I got the answer. Just to be sure of my answer I did the same with a side lenght of 13 and got 67 but the unknown doesn't look that big.

Please someone correct the used method since it feels not rigorous.

[alexnas]

that was honestly pretty easy, i figured out by looking at the other boxes and just realized its a difference of 6.

[danpryor]

I've needed and wanted this channel my whole life, it seems.

[mr.walterwhite]

Plz do more videos frequently like this sir

[vinaayagamkarunagaran]

Actually, there is an easier way. Firstly find the largest common factor for all the three given areas which is 6 since all the area has 2 same side length, one same side length is 6. Now just multiply 6 by 2 to find the length of one side of the square. Now just square 12. Then simply minus 144 by the given areas to find the last area.

[kenbrohere]

I did it in my head just by noticing the blue section was slightly smaller than than the largest.

[panosntop]

Can i solve the problem if i draw the line from the left side of the cube to the right that divides the cube in half and then work with trapeziums and triangles??don t know the defination in english..

[tramhicks]

I can't hear what you have said. Turn your volume up please?

[Bussiness_account]

I saw that the top left was 6 less than the top right corner, so I guessed the bottom left would be 6 less than the bottom right corner,
And I was right 😂. Did anyone else see this?
p.s. you could also do this vertically.

[firelion]

I actually thought it had something to do with the 6 times table.
24=4x6
30=5x6
48=8x6
He unknown area bust be either 7x or 9x, but since it is slightly smaller than the bottom right area and a lot bigger than the top right area, I figured, it must be 7x6, which is 42. A bit unscientific, but worked nonetheless