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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?"

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?

Given the products of adjacent cells, can you complete this Sudoku?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Given the products of diagonally opposite cells - can you complete this Sudoku?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

The clues for this Sudoku are the product of the numbers in adjacent squares.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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!

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Can you substitute numbers for the letters in these sums?

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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?

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

Number problems at primary level that require careful consideration.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

This Sudoku, based on differences. Using the one clue number can you find the solution?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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

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

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.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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.