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

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

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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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Can you work out what step size to take to ensure you visit all the dots on the circle?

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

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

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

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

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

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

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

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

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

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

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

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

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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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Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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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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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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An environment which simulates working with Cuisenaire rods.

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

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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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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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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

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

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

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Here is a chance to create some Celtic knots and explore the mathematics behind them.

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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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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?