Difference between revisions of "2004 IMO Problems/Problem 3"
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+ | == 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. | 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); | unitsize(0.5 cm); | ||
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draw((2,1)--(2,3)); | draw((2,1)--(2,3)); | ||
draw((3,1)--(3,3)); | draw((3,1)--(3,3)); | ||
− | + | </asy> | |
+ | |||
Determine all <math>m \times n</math> rectangles that can be covered without gaps and without overlaps with hooks such that; | Determine all <math>m \times n</math> rectangles that can be covered without gaps and without overlaps with hooks such that; | ||
(a) the rectangle is covered without gaps and without overlaps, | (a) the rectangle is covered without gaps and without overlaps, | ||
(b) no part of a hook covers area outside the rectangle. | (b) no part of a hook covers area outside the rectangle. | ||
+ | |||
+ | ==Solution== | ||
+ | {{solution}} | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=2004|num-b=2|num-a=4}} |
Latest revision as of 23:53, 18 November 2023
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.
Determine all 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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See Also
2004 IMO (Problems) • Resources | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
All IMO Problems and Solutions |