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

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

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

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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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Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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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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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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Can you substitute numbers for the letters in these sums?

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Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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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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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can 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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This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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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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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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Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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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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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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Using the statements, can you work out how many of each type of rabbit there are in these pens?

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There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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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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This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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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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Number problems at primary level that require careful consideration.

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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 group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

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Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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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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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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A few extra challenges set by some young NRICH members.

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Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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