IOM 2019, Блиц — Задача 24

OLYMPIAD OF METROPOLISES, Moscow, September 2, 2019 · 2 септември 2019 г.

Условие

Andrew and Bob are given a number $n$. Andrew and Bob take turns, Andrew takes the first turn. On his turn a player chooses $d$ such that $d$ is a natural number ranging from 1 to $n-1$ and d is a divisor of $n$. Then $d$ is subtracted from $n$. The player who can’t make a move loses. For which values of n Andrew can win no matter how Bob plays? (Multiple choice)

1. 2;

2. 3;

3. 2018;

4. 2019;

Решение

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Оригинал в Архива: blitz-en-all-task-final.pdf