Find the values of the nine letters in the sum: FOOT + BALL = GAME

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

What could the half time scores have been in these Olympic hockey matches?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Can you substitute numbers for the letters in these sums?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Number problems at primary level that require careful consideration.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Can you replace the letters with numbers? Is there only one solution in each case?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?