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?

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?

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?

Number problems at primary level that may require resilience.

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

Number problems at primary level to work on with others.

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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

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?

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?

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

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.

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

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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

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?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

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?

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

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

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?

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

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

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?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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.

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?

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

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

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

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?

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

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

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?

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?

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

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?

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?

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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.

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?

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

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