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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What is the smallest number with exactly 14 divisors?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
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?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
Can you find a way to identify times tables after they have been shifted up?
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?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
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?
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 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?
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Can you find any perfect numbers? Read this article to find out more...
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?
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.
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 the highest power of 11 that will divide into 1000! exactly.
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
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.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
A game that tests your understanding of remainders.
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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!?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Can you work out what size grid you need to read our secret message?
Substitution and Transposition all in one! How fiendish can these codes get?
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.
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. . . .
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. . . .
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?