yaworsw/euler-manager

---
:id: 344
:name: Silver dollar game
:url: https://projecteuler.net/problem=344
:content: "One variant of N.G. de Bruijn's **silver dollar** game can be described
  as follows:\n\nOn a strip of squares a number of coins are placed, at most one coin
  per square. Only one coin, called the **silver dollar** , has any value. Two players
  take turns making moves. At each turn a player must make either a _regular_ or a
  _special_ move.\n\nA _regular_ move consists of selecting one coin and moving it
  one or more squares to the left. The coin cannot move out of the strip or jump on
  or over another coin.\n\nAlternatively, the player can choose to make the _special_
  move of pocketing the leftmost coin rather than making a regular move. If no regular
  moves are possible, the player is forced to pocket the leftmost coin.\n\nThe winner
  is the player who pockets the silver dollar.\n\n ![p344_silverdollar.gif]({{ images_dir
  }}/p344_silverdollar.gif)  \n\nA _winning configuration_ is an arrangement of coins
  on the strip where the first player can force a win no matter what the second player
  does.\n\nLet W(<var>n</var>,<var>c</var>) be the number of winning configurations
  for a strip of <var>n</var> squares, <var>c</var> worthless coins and one silver
  dollar.\n\nYou are given that W(10,2) = 324 and W(100,10) = 1514704946113500.\n\nFind
  W(1 000 000, 100) modulo the semiprime 1000 036 000 099 (= 1 000 003 · 1 000 033).\n\n"