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?

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

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?

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

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

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

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

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.

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

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?

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

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

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?

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?

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?

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

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.

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?

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?

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.

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

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?

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?

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

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?

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

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?

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

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?

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?

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

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?

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

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?

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

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.

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

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?

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?

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?

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.

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

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

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.

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.