Question: The largest 2-digit number is 99. How many 2-digit numbers must be in a set in order to apply the pigeonhole principle to conclude that

The largest 2-digit number is 99. How many 2-digit numbers must be in a set in order to apply the pigeonhole principle to conclude that there are two distinct subsets of the numbers whose elements sum to the same value? You may need a calculator for this.

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