See if you can anticipate successive 'generations' of the two animals shown here.
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Here's a neat trick you can do with an 11 by 11 square...
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.
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
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.
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.
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
