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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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

Page

Toolbox

Search

1974 IMO Problems/Problem 4

Problem

Solution

See Also