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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 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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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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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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

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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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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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Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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Can you substitute numbers for the letters in these sums?

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

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

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

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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!

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

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

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

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

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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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If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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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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How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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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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Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

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In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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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?