# 欧拉计划：格子路径0919

„Starting in the top left corner of a 2×2 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 20×20 grid?“

$$W = {w_1, …, w_{2^n}}, \, w_k = p_1 \cdots p_{2\cdot n}, \, p_k \in \{ R, D \}.$$

$$\binom{2\cdot n}{n} = \frac{(2\cdot n)!}{n!\cdot n!}$$

$$\frac{(40)!}{20!\cdot 20!} = 137846528820.$$

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