Visualising and representing

problem

Logo Challenge - Triangles-Squares-Stars

Age

11 to 16

Challenge level

2 out of 3

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.
problem

11×11 Square

Age

11 to 16

Challenge level

2 out of 3

Here's a neat trick you can do with an 11 by 11 square...
game

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

Age

11 to 18

Challenge level

1 out of 3

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

1 out of 3

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

1 out of 3

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

Instant Insanity

Age

11 to 18

Challenge level

3 out of 3

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

1 out of 3

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

1 out of 3

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

1 out of 3

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

Changing Places

Age

14 to 16

Challenge level

1 out of 3

Place a red counter in the top left corner of a 4×4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?