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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Sets of Numbers

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### Prime Magic

### Diagonal Trace

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 7 to 11

Challenge Level

How many different sets of numbers with at least four members can you find in the numbers in this box?

For example, one set could be multiples of $4$ {$8, 36 ...$}, another could be odd numbers {$3, 13 ...$}.

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?