IMO Shortlist 1974 problem 11

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Dodao/la: arhiva
2. travnja 2012.
We consider the division of a chess board 8 \times 8 in p disjoint rectangles which satisfy the conditions:

a) every rectangle is formed from a number of full squares (not partial) from the 64 and the number of white squares is equal to the number of black squares.

b) the numbers \ a_{1}, \ldots, a_{p} of white squares from p rectangles satisfy a_1, , \ldots, a_p. Find the greatest value of p for which there exists such a division and then for that value of p, all the sequences a_{1}, \ldots, a_{p} for which we can have such a division.

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Izvor: Međunarodna matematička olimpijada, shortlist 1974