Question 51
There is a pile of $1000$ matches. Two players each take turns and can take up to $5$ matches. It is also allowed at most $10$ times during the whole game to take $6$ matches. (There are no restrictions who uses this possibility, for example $1$ exceptional move can be done by the first player, and, say, $3$ moves by the second.) Whoever takes the last match wins. Determine who wins this game.