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

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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?

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

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

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

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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.

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

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By selecting digits for an addition grid, what targets can you make?

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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

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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?

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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?

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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?

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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?

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

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

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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?"

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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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?

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

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

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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?

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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.

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

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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?

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This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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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.

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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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

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An investigation that gives you the opportunity to make and justify predictions.

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

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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?

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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.

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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...

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

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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.

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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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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?

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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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

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

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

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