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In order to dig half a hole, he first has to dig a quarter of a hole.
In order to dig a quarter of a hole, he first has to dig an eighth of a hole.
In order to dig eighth of a hole, he first has to dig 1/16 of a hole.
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In order to dig 1/N of a hole, he first has to dig 1/2xN of a hole.
IOW, he can not even leave home, let alone find a shovel, or walk to the work site.
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