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.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
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.
Can you substitute numbers for the letters in these sums?
Can you replace the letters with numbers? Is there only one
solution in each case?
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.
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?
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?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Find the sum of all three-digit numbers each of whose digits is
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Follow the clues to find the mystery number.
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?
What is the sum of all the digits in all the integers from one to
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.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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?
There are six numbers written in five different scripts. Can you
sort out which is which?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Nowadays the calculator is very familiar to many of us. What did
people do to save time working out more difficult problems before
the calculator existed?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Replace each letter with a digit to make this addition correct.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
There are two forms of counting on Vuvv - Zios count in base 3 and
Zepts count in base 7. One day four of these creatures, two Zios
and two Zepts, sat on the summit of a hill to count the legs of. . . .
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
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?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
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 the values of the nine letters in the sum: FOOT + BALL = GAME
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
Powers of numbers behave in surprising ways. Take a look at some of
these and try to explain why they are true.
Using balancing scales what is the least number of weights needed
to weigh all integer masses from 1 to 1000? Placing some of the
weights in the same pan as the object how many are needed?
How many six digit numbers are there which DO NOT contain a 5?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.