How many squares can be drawn on a checkers board, given that these squares should consist of whole black-white squares (the ones that are already painted on the board)?
So for a given square of size NxN, we can try to count up how many possible squares of that size will fit inside of an 8x8 board by calculating all the possible positions for the top-left corner of the smaller square. (call this F(N)...)
For example, there are 4 ways for a 7x7 square to be placed into an 8x8 square.
F(N) is (8-N+1)².
The TOTAL number of squares is the sum from 1 to 8 of F(N).
Right?
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Posted by levik
on 2002-11-19 07:23:03 |
Squares
