There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
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 make square numbers by adding two prime numbers together?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
Number problems at primary level to work on with others.
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?
Number problems at primary level that may require resilience.
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
If you have only four weights, where could you place them in order to balance this equaliser?
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.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Given the products of adjacent cells, can you complete this Sudoku?
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!
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 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?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you explain the strategy for winning this game with any target?
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 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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you work out some different ways to balance this equation?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A