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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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!
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
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?
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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
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?
Can you make square numbers by adding two prime numbers together?
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?
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.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Ben has five coins in his pocket. How much money might he have?
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?
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!
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
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.?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you substitute numbers for the letters in these sums?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In how many ways can you stack these rods, following the rules?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Can you use the information to find out which cards I have used?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This dice train has been made using specific rules. How many different trains can you make?
What happens when you round these three-digit numbers to the nearest 100?
In this matching game, you have to decide how long different events take.
The pages of my calendar have got mixed up. Can you sort them out?
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?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.