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Problem 161

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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?

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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？

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