Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Follow the clues to find the mystery number.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you make square numbers by adding two prime numbers together?
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?
Can you work out some different ways to balance this equation?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you replace the letters with numbers? Is there only one
solution in each case?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you substitute numbers for the letters in these sums?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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?
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 task depends on groups working collaboratively, discussing and reasoning to agree a final product.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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.
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?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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 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 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.