1974 IMO Problems/Problem 4

Problem

Consider decompositions of an $8\times8$ chessboard into $p$ non-overlapping rectangles subject to the following conditions:

(i) Each rectangle has as many white squares as black squares.

(ii) If $a_i$ is the number of white squares in the $i$-th rectangle, then $a_1<a_2<\cdots<a_p.$

Find the maximum value of $p$ for which such a decomposition is possible. For this value of $p,$ determine all possible sequences $a_1, a_2, \cdots, a_p.$

Solution

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See Also

1974 IMO (Problems) • Resources)
Preceded by
Problem 3
1 2 3 4 5 6 Followed by
Problem 5
All IMO Problems and Solutions
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