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

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Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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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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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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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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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Can you explain the strategy for winning this game with any target?

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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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A collection of resources to support work on Factors and Multiples at Secondary level.

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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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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

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The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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

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What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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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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A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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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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Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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

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List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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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 in which players take it in turns to choose a number. Can you block your opponent?

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Follow this recipe for sieving numbers and see what interesting patterns emerge.

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You'll need to know your number properties to win a game of Statement Snap...

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

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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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A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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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...

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

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

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How many zeros are there at the end of the number which is the product of first hundred positive integers?

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Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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Is there an efficient way to work out how many factors a large number has?

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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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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?