How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge extends the Plants investigation so now four or more children are involved.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
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 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?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Follow the clues to find the mystery number.
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 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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Find out what a "fault-free" rectangle is and try to make some of
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?
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?
An investigation that gives you the opportunity to make and justify
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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 replace the letters with numbers? Is there only one
solution in each case?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge is about finding the difference between numbers which have the same tens digit.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Can you find the chosen number from the grid using the clues?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?