Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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 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 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!
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Number problems at primary level that require careful consideration.
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you arrange 5 different digits (from 0 - 9) in the cross in 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.
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?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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?
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.
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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
An investigation that gives you the opportunity to make and justify
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?