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?

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

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

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.

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

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

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

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?

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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?

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?

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

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?

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

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?

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

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

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

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible 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.

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?

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

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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

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

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.

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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 beat the computer in the challenging strategy game?

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

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?

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?

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?

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

56 406 is the product of two consecutive numbers. What are these two numbers?