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?
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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!
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 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
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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 plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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?
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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 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?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
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?
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.
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?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Can you substitute numbers for the letters in these sums?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
My coat has three buttons. How many ways can you find to do up all
Can you use the information to find out which cards I have used?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?