ISAAC PLACES SOME COUNTERS ONTO THE SQUARES OF AN 8 BY 8 CHESSBOARD...

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