Thinking Cap

Problem of the Month

Winners of the academic year 2022/23 are Matthew Hudson and Jacob Norris.

December 2023

Thurston's Pentagon

Suppose that each vertex of a pentagon is given an integer in such a way that the sum of the five numbers is positive. Given three consecutive vertices with integers a, b, c for which b<0, an allowable move is one where you replace a, b, c by a+b, -b, b+c (respectively). Is there always a finite sequence of allowable moves which makes all five integers positive? Prove it or give a counterexample.