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

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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 sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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

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

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

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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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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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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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Number problems at primary level to work on with others.

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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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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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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 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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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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Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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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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Number problems at primary level that may require resilience.

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

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

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

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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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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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Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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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?"

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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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Got It game for an adult and child. How can you play so that you know you will always win?

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Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

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

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

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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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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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Find the highest power of 11 that will divide into 1000! exactly.

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Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

This article for teachers describes how number arrays can be a useful representation for many number concepts.