Combinations

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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?

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?