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?
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?
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.
Number problems at primary level that may require resilience.
Have a go at balancing this equation. Can you find different ways of doing it?
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 make square numbers by adding two prime numbers together?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Number problems at primary level to work on with others.
Follow the clues to find the mystery number.
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?
Can you find different ways of creating paths using these paving slabs?
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?
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?
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.
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
An investigation that gives you the opportunity to make and justify predictions.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
How many different rectangles can you make using this set of rods?
This article for teachers describes how number arrays can be a useful representation for many number concepts.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
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...
Find the highest power of 11 that will divide into 1000! exactly.