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

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In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

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

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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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

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

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

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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You have 5 darts and your target score is 44. How many different ways could you score 44?

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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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Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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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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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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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.

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What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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

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Play this game to learn about adding and subtracting positive and negative numbers

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A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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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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In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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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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Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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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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Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!

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Try out this number trick. What happens with different starting numbers? What do you notice?

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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?

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This task follows on from Build it Up and takes the ideas into three dimensions!

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What happens when you add a three digit number to its reverse?

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Try out some calculations. Are you surprised by the results?