Saturday, December 19, 2009

Prepare to square off

Consider an 8x8 chess board as shown in the adjacent figure. How many squares can you count without repetition?





Now consider the infinite chess board shown in the next figure. What is the inverse of the sum of the squares of all the distinct areas of squares that can formed from this board? What is the inverse of the sum of squares of all the square areas that can be formed from this board?

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3 Comments:

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Anonymous Sai said...

The answer to the first problem is 204. (1^2 + 2^2 +...+ 8^2)
As for the second problem, I'm guessing it is lt n->inf, 6/n(n+1)(2n+1), which is trivially 0, but I doubt I've read the problem correctly.

Mon May 10, 03:28:00 AM 2010  

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