### All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

# Blockupied

##### Stage: 3 and 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

A $1\times2\times3$ block is placed on an $8\times8$ board, as shown with the $1\times2$ face $X$ at the bottom. It is rolled over an edge without slipping onto a $1\times3$ face $Y$, then onto the $2\times3$ face $Z$,then onto $X$, $Y$, $Z$ again in that order. How many different squares on the board has the block occupied altogether, including the starting and ending positions?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.