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I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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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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Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

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Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

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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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Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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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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One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

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

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

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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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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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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 words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

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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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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.

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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?

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

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

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

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

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

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Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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

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This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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56 406 is the product of two consecutive numbers. What are these two numbers?

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

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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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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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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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Explore the relationship between simple linear functions and their graphs.