### Spiral Snail

A snail slithers around on a coordinate grid. At what position does he finish?

### Bucket of Water

Lisa's bucket weighs 21 kg when full of water. After she pours out half the water it weighs 12 kg. What is the weight of the empty bucket?

### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

# Straight Line Spin

##### Age 11 to 14 Short Challenge Level:

Geometrically:

The lines are perpendicular, so the new line slopes downwards at $45^\circ$, so its gradient is $-1$

It passes through $(1,1)$ so it also passes through $(0,2)$

Equation $y=-x+2$

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.