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?
Follow the clues to find the mystery number.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Have a go at balancing this equation. Can you find different ways of doing it?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Number problems at primary level that require careful consideration.
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Can you work out some different ways to balance this equation?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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!
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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.
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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?
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.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Can you make square numbers by adding two prime numbers together?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
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?
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.
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?
Can you substitute numbers for the letters in these sums?
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.