yaworsw/euler-manager

---
:id: 366
:name: Stone Game III
:url: https://projecteuler.net/problem=366
:content: "Two players, Anton and Bernhard, are playing the following game.  \nThere
  is one pile of n stones.  \nThe first player may remove any positive number of stones,
  but not the whole pile.  \nThereafter, each player may remove at most twice the
  number of stones his opponent took on the previous move.  \nThe player who removes
  the last stone wins.\n\nE.g. n=5  \nIf the first player takes anything more than
  one stone the next player will be able to take all remaining stones.  \nIf the first
  player takes one stone, leaving four, his opponent will take also one stone, leaving
  three stones.  \nThe first player cannot take all three because he may take at most
  2x1=2 stones. So let's say he takes also one stone, leaving 2. The second player
  can take the two remaining stones and wins.  \nSo 5 is a losing position for the
  first player.  \nFor some winning positions there is more than one possible move
  for the first player.  \nE.g. when n=17 the first player can remove one or four
  stones.\n\nLet M(n) be the maximum number of stones the first player can take from
  a winning position _at his first turn_ and M(n)=0 for any other position.\n\n∑M(n)
  for n≤100 is 728.\n\nFind ∑M(n) for n≤10<sup>18</sup>. Give your answer modulo 10<sup>8</sup>.\n\n"