Can you substitute numbers for the letters in these sums?
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.
There are lots of different methods to find out what the shapes are worth - how many can you find?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
This task follows on from Build it Up and takes the ideas into three dimensions!
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Number problems at primary level that require careful consideration.
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.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you replace the letters with numbers? Is there only one solution in each case?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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!
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?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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!
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
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 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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
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?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Can you use the information to find out which cards I have used?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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 smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?