In a sequence with 101 elements show that one can find an increasing sequence of 11 terms. Here is my approach: Pick the greatest element of the sequence (or one of the largest elements if there is more than one large element) and put it onto the end of the sequence we are forming. Then make ten groups consisting of the terms of the original sequence so that each group has ten elements. Now find the least elements of each group(if there is more than one least element in a group, then choose one of them). Finally, arranging these 10 least elements in an increasing order we get an increasing sequence of 11 terms. Is this argument sound? Or can we solve this problem in a more elegant way?