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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge is about finding the difference between numbers which have the same tens digit.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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.
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.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below 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!
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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 your way through the grid starting at 2 and following these
operations. What number do you end on?
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 cards 2, 4, 6, 8, +, - and =, what number statements can
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!
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Find all the numbers that can be made by adding the dots on two dice.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?