Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
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?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Can you find the chosen number from the grid using the clues?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this
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?
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?
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!
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
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?
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!
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
In this matching game, you have to decide how long different events take.
Try this matching game which will help you recognise different ways of saying the same time interval.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
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.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all
How many trains can you make which are the same length as Matt's, using rods that are identical?
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....?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Find out what a "fault-free" rectangle is and try to make some of
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?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.