MathDB
Navi and Ozna

Source: Junior Olympiad of Malaysia Shortlist 2015 C7 (JOM P5)

July 17, 2015
combinatoricsCombinatorial games

Problem Statement

Navi and Ozna are playing a game where Ozna starts first and the two take turn making moves. A positive integer is written on the waord. A move is to (i) subtract any positive integer at most 2015 from it or (ii) given that the integer on the board is divisible by 20142014, divide by 20142014. The first person to make the integer 00 wins. To make Navi's condition worse, Ozna gets to pick integers aa and bb, a≥2015a\ge 2015 such that all numbers of the form an+ban+b will not be the starting integer, where nn is any positive integer.
Find the minimum number of starting integer where Navi wins.
Back to ProblemsView on AoPS