The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

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.

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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?

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Use the information to work out how many gifts there are in each pile.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Use these four dominoes to make a square that has the same number of dots on each side.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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.

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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

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?

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.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.