Reflections

problem
Favourite

...on the Wall

Age

11 to 14

Challenge level

Explore the effect of reflecting in two intersecting mirror lines.
problem
Favourite

Surprising Transformations

Age

14 to 16

Challenge level

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
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

Cushion Ball

Age

16 to 18

Challenge level

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
problem

Retracircles

Age

16 to 18

Challenge level

Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.
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

Hidden Meaning

Age

7 to 11

Challenge level

What is the missing symbol? Can you decode this in a similar way?
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

Tricircle

Age

14 to 16

Challenge level

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.
problem

Two Triangles in a Square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.