Rotations

problem
Favourite

Rollin' Rollin' Rollin'

Age

11 to 14

Challenge level

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
problem
Favourite

Robotic Rotations

Age

11 to 16

Challenge level

How did the the rotation robot make these patterns?
problem
Favourite

Attractive Tablecloths

Age

14 to 16

Challenge level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem

Coke Machine

Age

14 to 16

Challenge level

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

Weighty Problem

Age

11 to 14

Challenge level

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.
problem

Middle Man

Age

16 to 18

Challenge level

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?
problem

Rots and Refs

Age

16 to 18

Challenge level

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
problem

Patchwork Quilt

Age

7 to 14

Challenge level

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?
problem

A Roll of Patterned Paper

Age

14 to 16

Challenge level

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
problem

Rearrange the Square

Age

5 to 7

Challenge level

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?