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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Primary Toughnuts

We sometimes have unsolved problems which require solutions. If there are any below, do consider having a go at them, and send us your solutions.

You may be interested in the article we have written, which explains what we are looking for when we decide which solutions to publish.

### Window Frames

### Sticky Dice

### Diagonal in a Spiral

### Painting Possibilities

### It's Times Again

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We sometimes have unsolved problems which require solutions. If there are any below, do consider having a go at them, and send us your solutions.

You may be interested in the article we have written, which explains what we are looking for when we decide which solutions to publish.

Age 5 to 14

Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Age 7 to 11

Challenge Level

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Age 7 to 11

Challenge Level

Investigate the totals you get when adding numbers in threes on the diagonal of this pattern.

Age 7 to 11

Challenge Level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

Age 7 to 14

Challenge Level

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!