math problem help?

Question

can anyone help me with this problem?
two players take turns removing one, two, or three cards from a pack. a player must never remove the same number of cards as has the previous player. the winner is the one either takes the last card o leaves the other player with no valid moves. is it an advantage to start if the pack has four cards? six cards?

Answer 1

If the pack has four cards, the second player can force a win. If the first player takes 1 or 3 cards, the second player simply takes the remaining cards for a win. If the first player takes 2 cards, the second player must take one card, leaving the first player with no legal moves.

If the pack has six cards, the first player can force a win by taking two cards and reducing it to the previous case. In addition, if they take 3 cards the second player must take either 1 or 2 and the first player will respectively take the 2 or 1 remaining cards. So the first player can force a win this way also.