Find the frequency distribution for ordinary English, and use it to help you crack the code.
Substitution and Transposition all in one! How fiendish can these codes get?
Can you work out what size grid you need to read our secret message?
A game that tests your understanding of remainders.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .
A collection of resources to support work on Factors and Multiples at Secondary level.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Have you seen this way of doing multiplication ?
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" .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
The clues for this Sudoku are the product of the numbers in adjacent squares.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
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
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
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.
Given the products of adjacent cells, can you complete this Sudoku?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you find a way to identify times tables after they have been shifted up?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Find the highest power of 11 that will divide into 1000! exactly.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .
Can you find any perfect numbers? Read this article to find out more...
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
What is the value of the digit A in the sum below: [3(230 + A)]^2 =