Notice that the squares don`t match up anymore, so you`ve got a rectangle made up of a bunch of squares and parts of squares. If you add up all of the fractions of squares, it will still add up to 64. Optical illusion.

The boxes which were sliced into two pieces aren`t exactly lined up in the second formation, so they are slight smaller than they should be. 65 boxes where some of them are slightly smaller = the same surface area as 64 boxes of the correct size.

Look at the top right corner; doesn`t line up correctly in the reordered grid. The rest of the issues are small to be noticeable with this resolution; each bisected box is something like 1/15 smaller.

Ok I`ve seen this before. The problem I have is that the new triangles created are shown as flush when laid on top of each other which is false. There would be a tiny quadrilateral hole with an area of 1^2. Thus, 64=65-1, because of said hole would exist when doing this the correct way meaning not in a way which it could be misinterpreted like this pic. give me a challenge!

the triangles and quadrilaterals do not have equal slopes, thus they cannot possibly form a correct 5x13 rectangle. this is stupid and has been around forever and is still not fooling anyone. not even a below average asian would believe this.

Knew that there was a little space between all of the pieces, but wanted to find all of the length of the sides of everything and all of the angles. Good math exercise for kids in school.

Took about 30 minutes of relearning the stuff and the calculations. There is a parallelogram in the middle. It`s area is exactly 1 unit square.

Could post picture of the calculations, but don`t feel like its really necessary as most people just know there is a small space is in there.

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It`s all in the slope. If you imagine the blue trapezoid as a 3x5 blue square attached to a 2x5 blue triangle, it makes sense. The red triangle has a slope of 3/8 (or 15/60). The blue triangle has a slope of 2/5 (or 16/60). This means that the hypotenuse of the 5x13 "triangle" they form is not a straight line, but bulges inward.

The area of this bulge is a triangle whose sides are the hypotenuses of the red, blue, and 5x13 triangle. If you use the pythagorean theorem to find the value of each hypotenuse (e.g. the hypotenuse of the red triangle is sqrt(3^2+8^2)=8.544), you can then plug those values into Heron`s formula (look it up if for some reason you don`t know it yet still care) to find the area of the triangle, which is 0.5. Do the same thing for the green triangle and orange trapezoid, which have the same dimensions, and you`ll get another 0.5.

- Those of you with an average amount of math smarts, prepare to have your minds blown.
The boxes which were sliced into two pieces aren`t exactly lined up in the second formation, so they are slight smaller than they should be. 65 boxes where some of them are slightly smaller = the same surface area as 64 boxes of the correct size.

Look at the top right corner; doesn`t line up correctly in the reordered grid. The rest of the issues are small to be noticeable with this resolution; each bisected box is something like 1/15 smaller.

Fancylad if f.ucking stupid

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My brain just broke.

And those of you with a decent level of math smarts, prepare to be annoyed at seeing this old trick again.

Took about 30 minutes of relearning the stuff and the calculations. There is a parallelogram in the middle. It`s area is exactly 1 unit square.

Could post picture of the calculations, but don`t feel like its really necessary as most people just know there is a small space is in there.

Predictable moaning aside, this is a nice take on an old puzzle that I hadn`t seen before. Good link, Fancy.

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The area of the gaps is equal to one square.

The area of this bulge is a triangle whose sides are the hypotenuses of the red, blue, and 5x13 triangle. If you use the pythagorean theorem to find the value of each hypotenuse (e.g. the hypotenuse of the red triangle is sqrt(3^2+8^2)=8.544), you can then plug those values into Heron`s formula (look it up if for some reason you don`t know it yet still care) to find the area of the triangle, which is 0.5. Do the same thing for the green triangle and orange trapezoid, which have the same dimensions, and you`ll get another 0.5.

0.5+0.5=1. Boom. I found your missing square.