Don't Say 21

How to play

1. Players count upward starting from 1.
2. On each turn, say one, two or three consecutive numbers.
3. The next player continues from the following number.
4. The player who is forced to say the losing number (21 by default) loses.
5. Change the losing number to explore how the winning pattern shifts.

Find the control numbers

Instead of thinking forward from 1, reason backward from the losing number. Ask which number you would like to hand to your opponent so that every possible reply can be answered. With a maximum of three numbers per turn, the strategic spacing between control positions is four: for 21 the control numbers are 20, 16, 12, 8 and 4.

Strategy tips

• Work backward before the game starts and identify the numbers you want to end your turns on.
• If the opponent says one number, answer with three; if they say two, answer with two; if they say three, answer with one.
• Changing the losing number tests whether you understand the pattern rather than memorizing one sequence.

Game-theory connection

This is a small impartial sequential game closely related to subtraction games. It demonstrates backward induction, winning and losing states, strategy invariants and how an apparently conversational game can have a precise mathematical solution.

Reading the screen

The number strip shows every number up to the losing one; each said number is coloured by the player who said it. The box at the bottom lists the most recent turns.