Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
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!
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!
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Choose a symbol to put into the number sentence.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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?
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?
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?
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?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
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 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!
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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.
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
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?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Find the sum of all three-digit numbers each of whose digits is odd.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
These two group activities use mathematical reasoning - one is numerical, one geometric.
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?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you substitute numbers for the letters in these sums?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
A game for 2 players. Practises subtraction or other maths operations knowledge.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.