How to play
Nim is played with four rows of matches: 1, 3, 5 and 7. Players take turns. On your turn, pick one row and take as many matches as you like from it, at least one. Tap a match: it and every match to its right are taken. The player who takes the last match wins.
That is the whole game. The first player moves first, and against the computer you are the first player. Hint shows a winning move when one exists, and Undo takes back one move against a friend, or your move together with the computer’s answer. Choose Friend at the top to play two people on one device.
Strategy
Nim is a solved game, and the solution is one of the prettiest tricks in mathematics.
- Write the row sizes in binary and add the columns without carrying (this is called the nim sum, or XOR). For 1, 3, 5, 7: 001, 011, 101, 111. Every column has an even number of ones, so the nim sum is 0.
- A position with nim sum 0 is lost for the player to move. Whatever they take, the sum becomes non-zero, and the opponent can always restore it to 0.
- To win, always leave a nim sum of 0. Find a row whose size changes the sum back to zero and reduce it to the right number.
- The opening position 1-3-5-7 has nim sum 0, so the second player wins with perfect play. The computer on the hard level never makes a mistake once it is ahead; on easy it sometimes does. Playing first, your best chance is to wait for a slip and then never let the sum leave zero again.
- Endgame shortcut. When only rows of size 1 remain, leave an even number of them. With two rows of equal size, mirror your opponent.
If you enjoy Nim, try Nine Men’s Morris or Okey next.
