If you have only four weights, where could you place them in order
to balance this equaliser?
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!
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Got It game for an adult and child. How can you play so that you know you will always win?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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?
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
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?
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?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This task follows on from Build it Up and takes the ideas into three dimensions!
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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!
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 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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
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?