2004 IMO Problems/Problem 3

Problem

Define a "hook" to be a figure made up of six unit squares as shown below in the picture, or any of the figures obtained by applying rotations and reflections to this figure.

$[asy] unitsize(0.5 cm); draw((0,0)--(1,0)); draw((0,1)--(1,1)); draw((2,1)--(3,1)); draw((0,2)--(3,2)); draw((0,3)--(3,3)); draw((0,0)--(0,3)); draw((1,0)--(1,3)); draw((2,1)--(2,3)); draw((3,1)--(3,3)); [/asy]$

Determine all $m \times n$ rectangles that can be covered without gaps and without overlaps with hooks such that; (a) the rectangle is covered without gaps and without overlaps, (b) no part of a hook covers area outside the rectangle.

Solution

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2004 IMO (Problems) • Resources
Preceded by Problem 2	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 4
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2004 IMO Problems/Problem 3

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