T For Two

Probability Level 3

S={1,7,13,19,25,,199}. S = \{1, 7, 13, 19, 25, \ldots , 199\}.

Find the least value nn such that for any subset TST \subset S with nn elements, we are guaranteed of finding two distinct elements of TT that sum to 206.

Clarification: The elements of SS are all integers of the form 6k+16k + 1 for all integers kk from 00 to 3333 inclusive.

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