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.
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.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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 you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
In this matching game, you have to decide how long different events take.
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 can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
The pages of my calendar have got mixed up. Can you sort them out?
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.
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
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
This dice train has been made using specific rules. How many different trains can you make?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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 arrange 5 different digits (from 0 - 9) in the cross in the
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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 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!
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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?
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?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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