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.
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?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you make square numbers by adding two prime numbers together?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Ben has five coins in his pocket. How much money might he have?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 use the information to find out which cards I have used?
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.
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.
Can you substitute numbers for the letters in these sums?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
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?
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 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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge is about finding the difference between numbers which have the same tens digit.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
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
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.