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# Arrangements

## Arrangements

In a 3 by 3 grid, it is possible to place some counters on the grid so that there is an even number of counters in every row and every column. (We are taking zero as an even number.)
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Age 7 to 11

Challenge Level

- Problem
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In a 3 by 3 grid, it is possible to place some counters on the grid so that there is an even number of counters in every row and every column. (We are taking zero as an even number.)

For which numbers of counters is this possible?

You may like to use this interactivity to explore your ideas.

Engaging with this problem will help children explain patterns they find linked with important properties of numbers.

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?