You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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 this Sudoku?
Can you work out what size grid you need to read our secret message?
A game that tests your understanding of remainders.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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?
How many zeros are there at the end of the number which is the
product of first hundred positive integers?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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.
Find the highest power of 11 that will divide into 1000! exactly.
Can you find a way to identify times tables after they have been shifted up?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Substitution and Transposition all in one! How fiendish can these codes get?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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. . . .
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
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?
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?
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). . . .
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
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. . . .
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?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Can you find any perfect numbers? Read this article to find out more...
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.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. . . .
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Follow this recipe for sieving numbers and see what interesting patterns emerge.