Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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.
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?
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" .
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Can you find any perfect numbers? Read this article to find out more...
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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?
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.
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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. . . .
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.
Have you seen this way of doing multiplication ?
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Can you find a way to identify times tables after they have been shifted up?
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). . . .
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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?
Can you find what the last two digits of the number $4^{1999}$ are?
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?
How many zeros are there at the end of the number which is the product of first hundred positive integers?
A game that tests your understanding of remainders.
Find the highest power of 11 that will divide into 1000! exactly.
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. . . .
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Explore the relationship between simple linear functions and their graphs.
Can you work out what size grid you need to read our secret message?
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. . . .
Substitution and Transposition all in one! How fiendish can these codes get?
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!?
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
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?
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.