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

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

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

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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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Two sudokus in one. Challenge yourself to make the necessary connections.

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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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The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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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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Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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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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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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Two sudokus in one. Challenge yourself to make the necessary connections.

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

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

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

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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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Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

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A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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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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A few extra challenges set by some young NRICH members.

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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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This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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

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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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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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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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Four small numbers give the clue to the contents of the four surrounding cells.