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When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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Play this game and see if you can figure out the computer's chosen number.

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

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How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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What is the smallest number of answers you need to reveal in order to work out the missing headers?

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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

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Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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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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The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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The clues for this Sudoku are the product of the numbers in adjacent squares.

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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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Find the number which has 8 divisors, such that the product of the divisors is 331776.

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Given the products of adjacent cells, can you complete this Sudoku?

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How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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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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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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

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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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How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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Number problems at primary level that may require resilience.

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The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Can you find any perfect numbers? Read this article to find out more...

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I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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

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A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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Number problems at primary level to work on with others.

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Can you work out what size grid you need to read our secret message?

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Can you find any two-digit numbers that satisfy all of these statements?

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

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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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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 work out some different ways to balance this equation?

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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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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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