MathDB
Removing Numbers On A Blackboard

Source: Bundeswettbewerb Mathematik 2017, Round 1 - #1

August 7, 2017
blackboardcombinatoricscombinatorics unsolvednumber theorynumber theory unsolveddivisibleDivisibility

Problem Statement

The numbers 1,2,3,,20171,2,3,\dots,2017 are on the blackboard. Amelie and Boris take turns removing one of those until only two numbers remain on the board. Amelie starts. If the sum of the last two numbers is divisible by 88, then Amelie wins. Else Boris wins. Who can force a victory?