Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 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 Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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!
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below 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
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.
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?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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 to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you use the information to find out which cards I have used?
Choose a symbol to put into the number sentence.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Ben has five coins in his pocket. How much money might he have?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Can you hang weights in the right place to make the equaliser
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Find all the numbers that can be made by adding the dots on two dice.
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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?
Can you substitute numbers for the letters in these sums?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.