Combinations

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?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

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?

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?