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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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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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There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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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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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.

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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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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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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

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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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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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Number problems at primary level that may require resilience.

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Number problems at primary level to work on with others.

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

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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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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Can you make square numbers by adding two prime numbers together?

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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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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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Can you work out some different ways to balance this equation?

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Have a go at balancing this equation. Can you find different ways of doing it?

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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

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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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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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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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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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

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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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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?

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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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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 activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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