Visualising and representing

problem
Favourite

Triangle in a Trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
problem
Favourite

Pythagoras Proofs

Age

11 to 16

Challenge level

Can you make sense of these three proofs of Pythagoras' Theorem?
problem
Favourite

Nine Colours

Age

11 to 16

Challenge level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
game

Yih or Luk Tsut K'i or Three Men's Morris

Age

11 to 18

Challenge level

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
problem

The Bridges of Konigsberg

Age

11 to 18

Challenge level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem

Triangles in the Middle

Age

11 to 18

Challenge level

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
problem

Instant Insanity

Age

11 to 18

Challenge level

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated.
problem

Natural Sum

Age

14 to 16

Challenge level

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
problem

Star Gazing

Age

14 to 16

Challenge level

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
problem

Penta Colour

Age

14 to 16

Challenge level

In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?