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

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?

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?

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?

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 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?

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?

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

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

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.

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

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?

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.

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?

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

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

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.

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?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

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

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

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

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?

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

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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.

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

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?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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?

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

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

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

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.

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

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

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

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

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?

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.

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.

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

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