# 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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