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Contests/Codeforces/Educational Codeforces Round 169/E. Not a Nim Problem
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Educational Codeforces Round 169

E. Not a Nim Problem

Game TheoryNumber TheoryArrayBit ManipulationDynamic Programming
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Solve on Codeforces

Problem Statement

Official algorithmic problem description and constraints.

Open on Codeforces

Two players, Alice and Bob, are playing a game. They have π‘› piles of stones, with the π‘–-th pile initially containing π‘Žπ‘– stones.

On their turn, a player can choose any pile of stones and take any positive number of stones from it, with one condition:

  • let the current number of stones in the pile be π‘₯. It is not allowed to take from the pile a number of stones π‘¦ such that the greatest common divisor of π‘₯ and π‘¦ is not equal to 1.

The player who cannot make a move loses. Both players play optimally (that is, if a player has a strategy that allows them to win, no matter how the opponent responds, they will win). Alice goes first.

Determine who will win.

Solutions & Walkthrough

Detailed video explanations, mathematical intuition, and clean C++ implementation code.

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