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?

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?

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?

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?

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

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

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?

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

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 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.

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?

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 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?

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

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?

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

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

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).

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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?

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

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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.

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

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

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?

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?

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 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.

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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.

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.

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?

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?

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

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?

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

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

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).

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

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.

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.

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 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?

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

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

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?