MathDB
ASU 256 All Soviet Union MO 1978 game with 2 heaps of checkers

Source:

July 11, 2019
game strategycombinatorics

Problem Statement

Given two heaps of checkers. the bigger contains mm checkers, the smaller -- nn (m>nm>n). Two players are taking checkers in turn from the arbitrary heap. The players are allowed to take from the heap a number of checkers (not zero) divisible by the number of checkers in another heap. The player that takes the last checker in any heap wins. a) Prove that if m>2nm > 2n, than the first can always win.
b) Find all xx such that if m>xnm > xn, than the first can always win.