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. . . .
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. . . .
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.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
What is the sum of all the digits in all the integers from one to
Find the values of the nine letters in the sum: FOOT + BALL = GAME
How can we help students make sense of addition and subtraction of negative numbers?
Find the numbers in this sum
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Replace each letter with a digit to make this addition correct.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
What is the sum of all the three digit whole numbers?
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
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
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.
There are nasty versions of this dice game but we'll start with the nice ones...
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you substitute numbers for the letters in these sums?
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.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Find a great variety of ways of asking questions which make 8.
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Using the 8 dominoes make a square where each of the columns and
rows adds up to 8
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
This number has 903 digits. What is the sum of all 903 digits?
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
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.