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

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

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

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

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

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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

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

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

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Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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

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

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

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

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

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

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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?

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

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

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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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Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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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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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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Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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What happens when you round these numbers to the nearest whole number?

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Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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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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Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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This dice train has been made using specific rules. How many different trains can you make?

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Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?