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?

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

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.

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

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?

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.

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.

There were 22 legs creeping across the web. How many flies? How many spiders?

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?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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

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

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.

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

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

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

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

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

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?

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

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

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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

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

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

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?

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

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.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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?

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?

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?

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 arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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.

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?

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?

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

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?

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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?