### 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?

# Various Venns

## Various Venns

Can you place the numbers from $0$ to $51$ into this Venn diagram?
How do you know where to put each number?
You might like to print off this sheet if you do not want to use the interactivity.

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Here is another one for you to try. If you'd prefer to work on paper, print off this sheet.
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The third Venn diagram below is a little different. This time you need to decide what sets the two groups represent. Choose the labels from the list on the right.

Here is a sheet you can print.
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Can you explain how you worked it out?

### Why do this problem?

The first two parts of this problem provide an opportunity for learners to become familiar with Venn diagrams, whilst reinforcing knowledge of number properties. The final part introduces slightly higher-level thinking as learners then work "backwards".

### Possible approach

If the group are not familiar with Venn diagrams, you could introduce them using this simple interactivity on an interactive whiteboard.

After the introduction learners could work on the problems either on paper or using the interactivity. If learners work on this in pairs it will encourage them to construct mathematical arguments to convince each other where on the diagram each number belongs. Explaining out loud in this way often helps to clarify thinking and will give a purpose for accurate use of mathematical vocabulary.

You could use the interactivity on an interactive whiteboard to help share their solutions in a plenary.

### Key questions

Learners could try their hands at placing numbers in a Venn diagram with three circles. They could use three categories such as 'multiples of $7$', 'square numbers' and 'odd numbers'. This sheet might be useful for this purpose.