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Problem 161


Problem 161


Triominoes

A triomino is a shape consisting of three squares joined via the edges. There are two basic forms:

If all possible orientations are taken into account there are six:

Any n by m grid for which nxm is divisible by 3 can be tiled with triominoes.
If we consider tilings that can be obtained by reflection or rotation from another tiling as different there are 41 ways a 2 by 9 grid can be tiled with triominoes:

In how many ways can a 9 by 12 grid be tiled in this way by triominoes?


三联骨牌

三联骨牌是由三个正方形方块拼接而成的骨牌,它一共有两种基本形状:

如果计入旋转,则一共有六种可能的形状:

任何n乘m的方阵,只要nxm能够被3整除,就能用三联骨牌拼出来。
如果我们认为翻转或旋转是不同的拼法,那一个2乘9的方阵有一共有41种拼法:

一个9乘12的方阵有多少种拼法?