Sunday, May 07, 2006

Geometry Puzzle

Does anyone out there know how to solve this puzzle? My friends and I are completely stumped by it.

Both the triangles are exactly the same size. The four portions are exactly the same size. How is it then, that when they are moved around, there is an extra square "hole" that appears?


Blogger Macht said...

It happens because the hypotenuse (in both pictures) isn't a straight line. Shape B goes horizontally 5 squares and vertically 2 squares while shape A goes horizontally 8 squares and vertically 3 squares. In order for the hypotenuse to be straight, they would have to have the same ratios. So in the top picture, the hypotenuse caves inwards while in the bottom picture, the hypotenuse caves outwards.

1:47 PM  
Blogger Keith said...


You are my new hero.

5:22 PM  
Anonymous Anonymous said...

Another way to explain it is that when you move C down so that its top row is now in line with the top row of D, it allows for one box to be unfilled. It does allow the triangle A and B to switch places, but via the previous post, that does not mean much.

6:12 AM  
Blogger AmericanPascal said...

This is a good example of self deception. On the surface we are inclined to make assumptions that we don’t even realize are being made – the picture (graph in this case) says a thousand words. But we are conditioned to read certain words or things into any picture we look at. However, when we start to analyze and to question our position, we often find the errors in our views. This is such a great example since the “obvious” missing square was in fact non-existent; and the explanation revealed the true error in our perception. This explains many things… if we could only see beyond the obvious.

7:37 PM  
Anonymous Anonymous said...

aNOTHER way to discover the problem is to realize that triangle "A" and triangle "B" can't possibly be similar triangles: one is 8x3, the other is 5x2. Since the 8/3 is not the same as 5/2, the acute angles must be different.

Basically, the "big triangle" made up of the four shapes combined is NOT a real triangle in either configuration.

2:40 PM  
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Anonymous Anonymous said...

Does anyone know the answer to this equation?

Three straight lines joined together so that they are rotated symmetric, four straight lines of three different lengths joined together so that they are vertically symmetric and then repeated later on, a semi-circle repeated later on, three straight lines joined together so that they are vertically symmetric, two straight lines joined
together to form a right-angle and three straight lines joined together so that they are laterally symmetric.

10:30 PM  

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