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?
Are these statements always true, sometimes true or never true?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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?
Number problems at primary level that may require determination.
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.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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 sum of all the three digit whole numbers?
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. . . .
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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. . . .
Find the numbers in this sum
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Find the sum of all three-digit numbers each of whose digits is
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.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use the information to work out how many gifts there are in each
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
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.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
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. . . .
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
What is happening at each box in these machines?