To Win This Numbers Game, Learn to Avoid Math Patterns

[Binary_Bark]

Here’s a simple number game to play on a rainy day, or while sheltering in place. You and I take turns crossing out numbers from the list {1, 2, 3, …, 9}. The winner is the last person to cross out a number without making three crossed-out numbers in a row. Let’s play! You can go first.


Suppose after four moves we’ve crossed out these numbers:


1 2 3 4 5 6 7 8 9


It’s your turn again. Notice if you cross out 4 you lose, as that makes three in a row: 3-4-5. You also lose if you cross out 7, as that makes 7-8-9. Your only safe plays are to cross out 1, 2 or 6. But no matter which number you choose, I can cross out one of the others and win by leaving you with no safe moves.

To Win This Numbers Game, Learn to Avoid Math Patterns

Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.

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