1. Isaac places some counters onto the squares of an 8 by 8 chessboard so
required, with complete proofs of any assertions
that there is at most one counter in each of the 64 squares. Determine,
you may make. Marks awarded will depend on the
with justification, the maximum number that he can place without
clarity of your mathematical presentation. Work
having five or more counters in the same row, or in the same column,
in rough first, and then write up your best attempt.
or on either of the two long diagonals.
Do not hand in rough work.
• One complete solution will gain more credit than
several unfinished attempts. It is more important
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