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2

Part of 2007 Swedish Mathematical Competition

Problems(1)

Andreas shaking hands and receiving flowers from n-1 persons

Source: 2007 Swedish Mathematical Competition p2

4/27/2021
A number of flowers are distributed between nn persons so that the first of them, Andreas, gets one flower, the other gets two flowers, the third gets three flowers, etc., to nn-th person who gets nn flowers. Andreas then walks around shaking hands with each other of the others, in any order. In order to do so, he receives a flower from everyone which he hangs on to and which has more flowers than himself at the moment they shake hands. Which is the smallest number of flowers Andreas can have after shaking hands with everyone?
combinatorics