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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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In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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

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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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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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Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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

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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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Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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

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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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You have 5 darts and your target score is 44. How many different ways could you score 44?

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

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

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

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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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Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

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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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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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If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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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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These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.