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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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Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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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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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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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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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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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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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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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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Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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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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Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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Here is a chance to play a version of the classic Countdown Game.

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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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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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Use these head, body and leg pieces to make Robot Monsters which are different heights.

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What do you notice about these squares of numbers? What is the same? What is different?

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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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Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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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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A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

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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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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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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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The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

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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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This challenge extends the Plants investigation so now four or more children are involved.

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Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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