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# What If...?

### Number Sandwiches

### More Number Sandwiches

### Shogi Shapes

### Robotic Rotations

### Nine Colours

### A Curious Collection of Bridges

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When were you last curious? What was it that provoked your curiosity?

We have chosen some problems for this feature that we hope will excite you and compel you to explore further. We hope you enjoy them!

Age 7 to 14

Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Age 11 to 16

Challenge Level

When is it impossible to make number sandwiches?

Age 11 to 14

Challenge Level

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

Age 11 to 16

Challenge Level

How did the the rotation robot make these patterns?

Age 11 to 16

Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 11 to 18

Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!