What is the Solution to Finding a Set of n+1 Integers from 2n?

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SUMMARY

The solution to finding a set of n+1 integers from the set {1, 2, ..., 2n} utilizes the classical pigeonhole principle. By partitioning the integers into disjoint subsets, such as {2k, 4k, 6k, ...} where k is an odd integer, one can ensure that each subset contains unique elements. This method guarantees that at least one subset will contain n+1 integers, fulfilling the requirements of the problem. The approach effectively demonstrates the application of combinatorial principles in integer selection.

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[SOLVED] Set of n+1 integers from 2n

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Classical pigeonhole argument. Write the set {1,2,...,2n} as a union of nice subsets, like those of the form {2k, 4k, 6k, ...} where k is an odd integer in {1,2,...,2n}. To apply the pigeonhole principle, we want these subsets to be disjoint. Can you find a way to do this?
 
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