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 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?

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?

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?

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?

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?

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.

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.

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

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

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

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

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?

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.

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

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

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.

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

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?

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

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

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?

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?

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

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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.

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.

Can you beat the computer in the challenging strategy game?

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?

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?

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?

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

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

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.

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.

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

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

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