Challenge Level

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.

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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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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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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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 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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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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When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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

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What is the sum of all the digits in all the integers from one to one million?

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A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

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

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

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

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The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .

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Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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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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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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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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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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Choose any three by three square of dates on a calendar page...

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Got It game for an adult and child. How can you play so that you know you will always win?

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

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

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You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

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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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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?

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Delight your friends with this cunning trick! Can you explain how it works?

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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. . . .

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This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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

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Can you explain the strategy for winning this game with any target?

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

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Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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

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Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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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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Using the 8 dominoes make a square where each of the columns and rows adds up to 8

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Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

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There are nasty versions of this dice game but we'll start with the nice ones...

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Here is a chance to play a fractions version of the classic Countdown Game.

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

How can we help students make sense of addition and subtraction of negative numbers?

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How many ways can you find to put in operation signs (+ - x Ã·) to make 100?