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This is a game for two players.

The first player chooses a positive even number that is less than $50$, and crosses it out on the grid.

The second player chooses a number to cross out. The number must be a factor or multiple of the first number.

Players continue to take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player.

The first person who is unable to cross out a number loses.

Here is an interactive version of the game in which you drag the numbers from the left hand grid and drop them on the right hand grid. Alternatively, click on a number in the left hand grid and it will transport to the earliest empty location in the right hand grid. You can rearrange the numbers in the right hand grid by dragging and dropping them in position. The integer in the top right hand corner grows with the number of factors/multiples you have in a row.

Alternatively, you can print out some 1-100 square grids.

Printable NRICH Roadshow resources: Instructions + Grid in 2 parts here and here.

An extension to the game, or a suitable activity for just one person, is suggested in the Possible extension in the Teachers' Notes.

Printable NRICH Roadshow resources: Instructions + Grid in 2 parts here and here.

An extension to the game, or a suitable activity for just one person, is suggested in the Possible extension in the Teachers' Notes.