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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Given the products of diagonally opposite cells - can you complete
The clues for this Sudoku are the product of the numbers in
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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. . . .
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
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.
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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.
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. . . .
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
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?
Explore the factors of the numbers which are written as 10101 in
different number bases. Prove that the numbers 10201, 11011 and
10101 are composite in any base.
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?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Find the highest power of 11 that will divide into 1000! exactly.
A game that tests your understanding of remainders.
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
Can you work out what size grid you need to read our secret message?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you find a way to identify times tables after they have been shifted up?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
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.
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
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...
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Substitution and Transposition all in one! How fiendish can these codes get?
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.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Can you find any perfect numbers? Read this article to find out more...
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Follow this recipe for sieving numbers and see what interesting patterns emerge.