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Number Detective

Follow the clues to find the mystery number.

Red Even

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Prime Magic

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?

Diagonal Trace

Age 7 to 11 Challenge Level:

Why do this problem?

This challenge is accessible to all pupils - everyone can have a go - but explaining why it is impossible with certain shapes is more difficult. It is a good context in which to encourage pupils to make conjectures and to verify them.

Key questions

Do you have a system fortrying to trace over the diagonals?
What do the shapes that work have in common?
Which other shapes do you think it will work for?

Possible extension

The problem Networks and Nodes would be a good follow-up challenge to this one.

Possible support

This sheet , with six of each shape and their diagonals drawn, will be useful to print off for some pupils.