Combinations

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

How many different shapes can you make by putting four right- angled isosceles triangles together?