Challenge Level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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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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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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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Can you work out some different ways to balance this equation?

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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An investigation that gives you the opportunity to make and justify predictions.

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Have a go at balancing this equation. Can you find different ways of doing it?

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"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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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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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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How many different sets of numbers with at least four members can you find in the numbers in this box?

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

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Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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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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Can you make square numbers by adding two prime numbers together?

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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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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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Number problems at primary level that may require resilience.

Challenge Level

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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In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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Can you find different ways of creating paths using these paving slabs?

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The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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Can you complete this jigsaw of the multiplication square?

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I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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Number problems at primary level to work on with others.

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Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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Given the products of diagonally opposite cells - can you complete this Sudoku?

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Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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Are these statements always true, sometimes true or never true?

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Factors and Multiples game for an adult and child. How can you make sure you win this game?

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"