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

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

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

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

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

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

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

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

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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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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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These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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

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

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

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

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

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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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Explore the relationship between simple linear functions and their graphs.

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

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

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

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

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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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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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I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

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6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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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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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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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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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.