When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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?

Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

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?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

How many six digit numbers are there which DO NOT contain a 5?

I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?

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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

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

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

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?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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.

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Can you find all the different ways of lining up these Cuisenaire rods?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?