Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Find out about palindromic numbers by reading this article.
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are
natural numbers and 0 < a < b < c. Prove that there is
only one set of values which satisfy this equation.
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
What is the last digit of the number 1 / 5^903 ?
How many six digit numbers are there which DO NOT contain a 5?
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?
Suppose you had to begin the never ending task of writing out the
natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the
1000th digit you would write down.
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
The number 10112359550561797752808988764044943820224719 is called a
'slippy number' because, when the last digit 9 is moved to the
front, the new number produced is the slippy number multiplied by
There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?
Can you make a hypothesis to explain these ancient numbers?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
This task depends on learners sharing reasoning, listening to
opinions, reflecting and pulling ideas together.
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.
Are these statements always true, sometimes true or never true?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
What are the last two digits of 2^(2^2003)?
Ranging from kindergarten mathematics to the fringe of research
this informal article paints the big picture of number in a non
technical way suitable for primary teachers and older students.
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.
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" .
Can you work out how many of each kind of pencil this student
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?
What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Can you find any perfect numbers? Read this article to find out more...
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Is there an efficient way to work out how many factors a large number has?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Problem one was solved by 70% of the pupils. Problem 2 was solved
by 60% of them. Every pupil solved at least one of the problems.
Nine pupils solved both problems. How many pupils took the exam?
Visitors to Earth from the distant planet of Zub-Zorna were amazed
when they found out that when the digits in this multiplication
were reversed, the answer was the same! Find a way to explain. . . .
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
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.
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. . . .
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.