In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
What are the missing numbers in the pyramids?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
Replace each letter with a digit to make this addition correct.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Delight your friends with this cunning trick! Can you explain how
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Can you explain how this card trick works?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Find the sum of all three-digit numbers each of whose digits is
Find the next number in this pattern: 3, 7, 19, 55 ...
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This is an adding game for two players.
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 what happens when you add house numbers along a street
in different ways.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
How can we help students make sense of addition and subtraction of negative numbers?
This number has 903 digits. What is the sum of all 903 digits?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Find a great variety of ways of asking questions which make 8.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the