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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
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
Find all the numbers that can be made by adding the dots on two dice.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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.
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!
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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.
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!
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This dice train has been made using specific rules. How many different trains can you make?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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?
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 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?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
There were 22 legs creeping across the web. How many flies? How many spiders?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?