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

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

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?

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

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 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.

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?

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

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).

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

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?

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

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?

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

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

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?

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

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

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

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?

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?

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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?

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?

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

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.

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.

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?

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.

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?

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.

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

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

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?

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

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?

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

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

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

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?

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.

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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?

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

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

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.

Use the information to work out how many gifts there are in each pile.