Split two peas in a pod

Probability Level 5

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

x1+x2++x19=x20? x_1 + x_2 + \ldots + x_{19} = x_{20}?

×

Problem Loading...

Note Loading...

Set Loading...