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Problem 208

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Robot Walks

A robot moves in a series of one-fifth circular arcs (72°), with a free choice of a clockwise or an anticlockwise arc for each step, but no turning on the spot.

One of 70932 possible closed paths of 25 arcs starting northward is

Given that the robot starts facing North, how many journeys of 70 arcs in length can it take that return it, after the final arc, to its starting position?
(Any arc may be traversed multiple times.)

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机器人走路

一个机器人每步走五分之一个圆弧（72°），它每步都可以选择顺时针走或是逆时针走，但在走的途中不能改变方向。

机器人从面向正北方开始，连续走25步所构成的闭合路径共有70932条，以下是其中一条：

假定机器人仍然从面向正北方开始，连续走70步之后，能够回到出发位置的路径有多少条？
（所有圆弧都可以经过多次。）

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