Andreas shaking hands and receiving flowers from n-1 persons
Source: 2007 Swedish Mathematical Competition p2
April 27, 2021
combinatorics
Problem Statement
A number of flowers are distributed between persons so that the first of them, Andreas, gets one flower, the other gets two flowers, the third gets three flowers, etc., to -th person who gets 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?