Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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.
56 406 is the product of two consecutive numbers. What are these two 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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
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?
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 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.
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.
Can you go from A to Z right through the alphabet in the hexagonal maze?
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?
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.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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?
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 the information to work out how many gifts there are in each pile.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
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?
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?
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?
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 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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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.
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 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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you use the information to find out which cards I have used?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?