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