Pile of gold coins

Logic Level 3

You play a game with a pile of \(N\) gold coins.

You and a friend take turns removing 1, 3, or 6 coins from the pile.
The winner is the one who takes the last coin.

For the person that goes first, how many winning strategies are there for \(N < 1000?\)

Clarification: For \(1 \leq N \leq 999\), for how many values of \(N\) can the first player develop a winning strategy?


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