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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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 make dice stairs using the rules stated? How do you know you have all the possible stairs?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Can you find all the ways to get 15 at the top of this triangle of numbers?

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 task follows on from Build it Up and takes the ideas into three dimensions!

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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?

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?

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.?

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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 jugs.

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!

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?

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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?