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# Fifteen

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Age 7 to 14

Challenge Level

- Game

Fifteen is a game for two players that you can play anywhere, anytime. Try it without writing anything down. You take it in turns to choose one of the whole numbers 1 to 9 (and each number can only be chosen once). To win you have to pick 3 numbers that add up to 15.

This is a game for two players.

Take it in turns to choose one of the whole numbers 1 to 9.

Each number can be chosen only once.

To win, you must have three numbers that add up to 15.

If each person has three numbers and neither player has a total of 15, continue playing until one of you has three of their digits totalling 15, or stalemate is reached.

If you want to see an example here is what happened when Safi and Lila played:

Safi chose 5

Lila chose 6

Safi had 5 and chose 4 making 9

Lila had 6 and chose 7 making 13

Safi had 9 and chose 4 making 13

Lila had 13 and so chose 2 to win!

Lila chose 6

Safi had 5 and chose 4 making 9

Lila had 6 and chose 7 making 13

Safi had 9 and chose 4 making 13

Lila had 13 and so chose 2 to win!

Can you analyse the structure in the following games and the correspondences between them? Describe the patterns that show they are equivalent games that can be played using equivalent strategies.

- Noughts and Crosses
- Online
- Fifteen
- Jam

We suggest tackling them in the order given.

Printable NRICH Roadshow resource.The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.