A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Follow the clues to find the mystery number.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Given the products of adjacent cells, can you complete this Sudoku?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Four small numbers give the clue to the contents of the four
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Investigate the different ways you could split up these rooms so
that you have double the number.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the