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 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.

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

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

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?

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

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.

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 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?

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?

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

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.

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

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

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

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?

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

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?

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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?

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.

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?

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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

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?

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

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.

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

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?

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

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

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make a 3x3 cube with these shapes made from small cubes?

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.

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.

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.