Pile of gold coins
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?