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.
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. . . .
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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. . . .
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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
Work out how to light up the single light. What's the rule?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
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. . . .
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
What are the last two digits of 2^(2^2003)?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
How many six digit numbers are there which DO NOT contain a 5?
What is the last digit of the number 1 / 5^903 ?
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?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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.
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 work out how many of each kind of pencil this student
Can you find any perfect numbers? Read this article to find out more...
Can you make a hypothesis to explain these ancient numbers?
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?
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 at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
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" .
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.
Find out about palindromic numbers by reading this article.
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.
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Can you find ways of joining cubes together so that 28 faces are
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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 task depends on learners sharing reasoning, listening to
opinions, reflecting and pulling ideas together.
Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.
Are these statements always true, sometimes true or never true?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.
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?