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

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

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.

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

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?

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

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

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

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?

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

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?

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 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?

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

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.

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

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

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

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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

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?

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 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?

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

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?

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?

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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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?

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?

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.

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?

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.

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.

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

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.

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).

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

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

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?

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

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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?

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

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?

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?

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.

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.