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

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

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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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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 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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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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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 group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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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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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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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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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 substitute numbers for the letters in these sums?

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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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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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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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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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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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Number problems at primary level that require careful consideration.

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

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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

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Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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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?

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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Ben has five coins in his pocket. How much money might he have?

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

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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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Have a go at balancing this equation. Can you find different ways of doing it?

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Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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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 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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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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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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On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.