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What is the smallest integer NNN, such that no matter how we split the set SN={1,2,…,N} S_N = \{ 1, 2, \ldots, N \} SN={1,2,…,N} into two sets A A A and BBB, there exists one set such that we can find 20 (not necessarily distinct) elements x1,x2,…x20 x_1, x_2, \ldots x_{20} x1,x2,…x20 satisfying
x1+x2+…+x19=x20? x_1 + x_2 + \ldots + x_{19} = x_{20}? x1+x2+…+x19=x20?
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