A game you can win

You and a friend take turns. Each adds 1, 2 or 3. First to say 22 wins. You go first. Start at 0.

The rule

Work backwards from 22. A winning number lets you win. Say 18, and your friend cannot reach 22. So 18 is a winning number. Each winning number is 4 less than the next one.

22 − 4 = 18. 18 − 4 = 14. 14 − 4 = 10. 10 − 4 = 6. 6 − 4 = 2.

Winning numbers: 2, 6, 10, 14, 18, 22. Say 2 first: add 2 to 0. Then say each winning number.

Example

You say 18. Your friend says 19, 20 or 21.

If your friend says 19, you add 3. If 20, add 2. If 21, add 1. You say 22 and win.

Each pair of turns adds up to 4.