Problem

Source: Indonesia IMO 2010 TST, Stage 1, Test 4, Problem 1

Tags: invariant, combinatorics proposed, combinatorics



The integers $ 1,2,\dots,20$ are written on the blackboard. Consider the following operation as one step: choose two integers $ a$ and $ b$ such that $ a-b \ge 2$ and replace them with $ a-1$ and $ b+1$. Please, determine the maximum number of steps that can be done. Yudi Satria, Jakarta