Can you replace the letters with numbers? Is there only one
solution in each case?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Follow the clues to find the mystery number.
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you substitute numbers for the letters in these sums?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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.
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?
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?
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?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you draw a square in which the perimeter is numerically equal
to the area?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you make square numbers by adding two prime numbers together?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Ben has five coins in his pocket. How much money might he have?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the