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?
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?
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?
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?
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?
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.
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 were 22 legs creeping across the web. How many flies? How many spiders?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
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.
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.
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.
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?
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?
Use the information to work out how many gifts there are in each pile.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
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?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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?
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?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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).
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?
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.
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?
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps 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?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.