What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
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.
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?
Can you substitute numbers for the letters in these sums?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Find the sum of all three-digit numbers each of whose digits is
You have two sets of the digits 0 – 9. Can you arrange these
in the five boxes to make four-digit numbers as close to the target
numbers as possible?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
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.
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?
What is the sum of all the digits in all the integers from one to
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
There are nasty versions of this dice game but we'll start with the nice ones...
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
There are six numbers written in five different scripts. Can you sort out which is which?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
Follow the clues to find the mystery number.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
What happens when you round these three-digit numbers to the nearest 100?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Explore the relationship between simple linear functions and their
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.