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Number Detective

Follow the clues to find the mystery number.

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Make 37

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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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?

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.