In the village, there are 100 houses. What is the maximum number of closed, non-intersecting fences that can be built so that each fence encloses at least one house and no two fences enclose the same set of houses?

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In the maximum set of fences, there is a fence that limits exactly two houses. By combining these two houses into one, we reduce the number of houses by 1 and the number of fences by 2. In this process, both conditions of the problem are maintained. Continue this process. After 99 steps, one house and one fence will remain. And we have removed 198 fences. Therefore, there were 199 in total.

## Answer

199 fences.