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?
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.?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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
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.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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?
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 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 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!
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
An investigation that gives you the opportunity to make and justify
The pages of my calendar have got mixed up. Can you sort them out?
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
In this matching game, you have to decide how long different events take.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What happens when you round these numbers to the nearest whole number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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 many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What happens when you round these three-digit numbers to the nearest 100?
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 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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.