Ten girls sit around a table
Source: South African MO 2009 Q3
May 26, 2012
pigeonhole principlecombinatorics unsolvedcombinatorics
Problem Statement
Ten girls, numbered from 1 to 10, sit at a round table, in a random order. Each girl then receives a new number, namely the sum of her own number and those of her two neighbours. Prove that some girl receives a new number greater than 17.