As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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

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

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?

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

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?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

Can you go from A to Z right through the alphabet in the hexagonal maze?

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

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.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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?

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?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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

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.

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?

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?

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

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?

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?

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?

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?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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

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

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?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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?

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?

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?

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?

What do you notice about these squares of numbers? What is the same? What is different?

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.

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?

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.