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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

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

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?

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

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

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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?

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?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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?"

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

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?

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

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

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

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

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?

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?

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?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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.

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?

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?

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?

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?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Number problems at primary level that may require resilience.

Number problems at primary level to work on with others.

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

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?

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.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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.

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?

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?

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?