Visualising and representing

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
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
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?
problem
Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Salinon

Age

14 to 16

Challenge level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
problem
Spotting the loophole

Age

14 to 16

Challenge level

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
problem
Efficient packing

Age

14 to 16

Challenge level

How efficiently can you pack together disks?
problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Building gnomons

Age

14 to 16

Challenge level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
problem
Slick summing

Age

14 to 16

Challenge level

Watch the video to see how Charlie works out the sum. Can you adapt his method?