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Problem 15

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Lattice paths

Starting in the top left corner of a $2\times2$ grid, and only being able to move to the right and down, there are exactly $6$ routes to the bottom right corner.

How many such routes are there through a $20\times20$ grid?

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网格路径

从一个$2\times2$网格的左上角出发，若只允许向右或向下移动，则恰好有$6$条抵达右下角的路径。

对于$20\times20$网格，这样的路径有多少条？

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