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In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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My coat has three buttons. How many ways can you find to do up all the buttons?

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El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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

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When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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Can you find out in which order the children are standing in this line?

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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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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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In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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Find all the numbers that can be made by adding the dots on two dice.

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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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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?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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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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Investigate the different ways you could split up these rooms so that you have double the number.

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My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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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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This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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This challenge is about finding the difference between numbers which have the same tens digit.

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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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Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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

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Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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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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Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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How many different rectangles can you make using this set of rods?

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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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Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.