« Vrati se
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.


Moderator says: see http://www.artofproblemsolving.com/Foru ... 41t=58591

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1176IMO Shortlist 1964 problem 41
1169IMO Shortlist 1963 problem 31
1168IMO Shortlist 1963 problem 21
1157IMO Shortlist 1961 problem 41
1153IMO Shortlist 1960 problem 71
1144IMO Shortlist 1959 problem 47