Coins in a Line

Problem

There are n coins in a line. Two players take turns to take one or two coins from right side until there are no more coins left. The player who take the last coin wins.

Could you please decide the first play will win or lose?

Example

• n = 1, return true.
• n = 2, return true.
• n = 3, return false.
• n = 4, return true.
• n = 5, return true.

Challenge

O(n) time and O(1) memory

Solution

Since you can take either 1 or 2 coins, the second player can always either 2 or 1 coins to make sure 3 coins are taken in one round, so if n % 3 == 0, the second player will win, otherwise the first player will win.