Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
The clues for this Sudoku are the product of the numbers in adjacent squares.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
A game that tests your understanding of remainders.
If you have only four weights, where could you place them in order
to balance this equaliser?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Use the interactivities to complete these Venn diagrams.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
An investigation that gives you the opportunity to make and justify
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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...
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
What is the smallest number with exactly 14 divisors?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you find a way to identify times tables after they have been shifted up?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?