Friday Puzzle #6

6 10 2011

A chess board has 8*8 squares with alternating black/white colors. The rows are labeled 1-8 and the columns are labeled A-H. The square A1 is black.

However, for the purpose of this week’s friday puzzle, let’s re-label the rows and columns with numbers starting from zero. Then, square (0,0) is black, as well as (1,1), (2,2), etc. Also, the chess board is not restricted to 8*8 squares, it can be arbitrarily large (yet finite), or N*N in size.

Then place pawns on the board according to the following rules:

  • Square (0,0) contains a pawn
  • If and only if square (0,X) contains a pawn, then square (X,0) contains a pawn
  • If and only if both squares (R,0) and (0,S) contain a pawn, then square (R,S) contains a pawn

When the pawns are correctly configured the total number of pawns will be a square number, and they will form a diagonally symmetric pattern. Some pawns will occupy a white square and others will occupy a black square. Call their difference the target.

The puzzle: What is the smallest board where a pattern can be created whose target is a prime number?

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