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?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
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?
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 ...?
Can you make square numbers by adding two prime numbers together?
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?
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?
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 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.
Ben’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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
How many different rectangles can you make using this set of rods?
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
Follow the clues to find the mystery number.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you find different ways of creating paths using these paving slabs?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
An investigation that gives you the opportunity to make and justify predictions.
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?
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?
Number problems at primary level to work on with others.
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?
Number problems at primary level that may require resilience.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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.
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.
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?
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 work out what a ziffle is on the planet Zargon?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?