Search ProblemsRSS Feed
projecteuler.net

Divisor game

Problem 550 Published on Saturday, 5th March 2016, 01:00 pm; Solved by 227;
Difficulty rating: 60%

Two players are playing a game. There are k piles of stones. When it is his turn a player has to choose a pile and replace it by two piles of stones under the following two conditions:

  • Both new piles must have a number of stones more than one and less than the number of stones of the original pile.
  • The number of stones of each of the new piles must be a divisor of the number of stones of the original pile.

The first player unable to make a valid move loses.
Let f(n,k) be the number of winning positions for the first player, assuming perfect play, when the game is played with k piles each having between 2 and n stones (inclusively).
f(10,5)=40085.

Find f(107,1012).
Give your answer modulo 987654321.