Let k≥3 be an integer. Prove that if n>(3k), then for any 3n pairwise different real numbers ai,bi,ci (1≤i≤n), among the numbers ai+bi, ai+ci, bi+ci, one can find at least k+1 pairwise different numbers. Show that this is not always the case when n=(3k). combinatorics unsolvedcombinatorics