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A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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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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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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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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Can you go from A to Z right through the alphabet in the hexagonal maze?

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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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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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Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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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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Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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Use the information to work out how many gifts there are in each pile.

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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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On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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

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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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If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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Can you use the information to find out which cards I have used?

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Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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You have a set of the digits from 0 â€“ 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

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Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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Can you make a 3x3 cube with these shapes made from small cubes?

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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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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

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Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

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Use the information about Sally and her brother to find out how many children there are in the Brown family.

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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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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

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Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?