I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

There are thirty six teddies in Teddy Town - six red, six blue, six yellow, six green, six purple and six turquoise. There are also thirty six houses, six of each colour. Can you put them on the map of Teddy Town according to the rules?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

There are sixteen teddies in Teddy Town - four red, four blue, four yellow and four green. There are also sixteen houses, four of each colour. Can you put them on the map of Teddy Town according to the rules?

There are twenty five teddies in Teddy Town - five red, five blue, five yellow, five green and five purple. There are also twenty five houses, five of each colour. Can you put them on the map of Teddy Town according to the rules?