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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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

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?

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

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.

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

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

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

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!

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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?

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

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

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

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?

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?

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

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?

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

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

Number problems at primary level that may require resilience.

Number problems at primary level to work on with others.

If you have only four weights, where could you place them in order to balance this equaliser?

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?

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

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

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?

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.

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

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?

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?

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 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?

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?