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 took.

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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?

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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.

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Can you use this information to work out Charlie's house 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!

There are lots of different methods to find out what the shapes are worth - how many can you find?

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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

This dice train has been made using specific rules. How many different trains can you make?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

How long does it take to brush your teeth? Can you find the matching length of time?

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.

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

The pages of my calendar have got mixed up. Can you sort them out?

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?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Ben has five coins in his pocket. How much money might he have?

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?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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.

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Can you use the information to find out which cards I have used?

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.?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

This article for primary teachers suggests ways in which to help children become better at working systematically.

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?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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