Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Can you explain the strategy for winning this game with any target?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
A game that tests your understanding of remainders.
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
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.
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
Have you seen this way of doing multiplication ?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
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
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?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
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 any perfect numbers? Read this article to find out more...
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
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. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
How many noughts are at the end of these giant numbers?
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. . . .
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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...
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?