Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these
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?
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.
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.
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?
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?
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?
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?
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
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
Use the information to work out how many gifts there are in each
There were 22 legs creeping across the web. How many flies? How many spiders?
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have 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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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?
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?
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?
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
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?