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National and Regional Contests
Chile Contests
Chile National Olympiad
1991 Chile National Olympiad
3
3
Part of
1991 Chile National Olympiad
Problems
(1)
18 dominoes in 6x6 board (Chile NMO 1991 P3)
Source:
11/20/2021
A board of
6
×
6
6\times 6
6
×
6
is totally covered by
18
18
18
dominoes (of
2
×
1
2\times 1
2
×
1
), that is, there are no overlaps, gaps, and the tiles do not come off the board. Prove that, regardless of the arrangement of the tiles, there is always a line that divides the board into two non-empty parts, and without cutting tiles.
Tiling
tiles
combinatorics