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

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

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

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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 task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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

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In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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

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

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

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Can you make square numbers by adding two prime numbers together?

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These two group activities use mathematical reasoning - one is numerical, one geometric.

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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 problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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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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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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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

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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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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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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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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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Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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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 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 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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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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How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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How many different rectangles can you make using this set of rods?

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How many possible necklaces can you find? And how do you know you've found them all?

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On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.