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These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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The Zargoes use almost the same alphabet as English. What does this birthday message say?

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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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These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

This article for primary teachers suggests ways in which to help children become better at working systematically.

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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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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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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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Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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

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These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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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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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

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

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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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What could the half time scores have been in these Olympic hockey matches?

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

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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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Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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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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My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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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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This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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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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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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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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There are lots of different methods to find out what the shapes are worth - how many can you find?

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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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This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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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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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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Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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