Follow the clues to find the mystery number.
Can you find the chosen number from the grid using the clues?
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?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Number problems at primary level that require careful consideration.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you replace the letters with numbers? Is there only one solution in each case?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you substitute numbers for the letters in these sums?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you work out some different ways to balance this equation?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
An investigation that gives you the opportunity to make and justify predictions.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Can you make square numbers by adding two prime numbers together?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
How many possible necklaces can you find? And how do you know you've found them all?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?