This Sudoku requires you to do some working backwards before working forwards.

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?

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

Number problems at primary level that require careful consideration.

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

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...

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?

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

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

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

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.

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?

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?

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

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?"

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

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

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

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!

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

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

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

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

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.

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

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Can you substitute numbers for the letters in these sums?

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?

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.

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?

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

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?

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

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

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

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.

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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