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Checkers trick (Posted on 2002-11-18) Difficulty: 2 of 5
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)?

  Submitted by Raveen    
Rating: 3.7500 (4 votes)
Solution: (Hide)
The total number of squares on the board is equal to the number of 1x1 squares (64) + the number of 2x2 squares + .... + number of 8x8 squares (1).

In general, the number of NxN squares on an 8x8 board can be obtained by figuring out the number possible positions for the upper-left corner of the smaller square. For example, if dealing with 7x7 squares, there are only 4 possible positions for its upper-left corner, and therefore, there are only 4 possible 7x7 squares on an 8x8 board.

A formula for this function F(N) is pretty easy to deduce: F(N) = (9-N)2

So, the overall sum is

F(1) + F(2) + F(3) + F(4) + F(5) + F(6) + F(7) + F(8) =
64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 =
204

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionProblem Solution With ExplanationK Sengupta2007-05-15 04:37:28
answerK Sengupta2007-05-15 04:33:32
AnswerLawrence2003-08-30 14:01:53
re: SquaresNick Reed2002-11-19 07:31:43
SolutionSquareslevik2002-11-19 07:23:03
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