How many noughts are at the end of these giant numbers?
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" .
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...
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
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?
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?
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?
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.
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). . . .
Is there an efficient way to work out how many factors a large number has?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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.
Can you find any perfect numbers? Read this article to find out more...
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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.
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. . . .
Can you work out what size grid you need to read our secret message?
Got It game for an adult and child. How can you play so that you know you will always win?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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 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?"
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.
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Can you explain the strategy for winning this game with any target?
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. . . .
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Can you find any two-digit numbers that satisfy all of these statements?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Find the highest power of 11 that will divide into 1000! exactly.
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. . . .
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
How did the the rotation robot make these patterns?
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?
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.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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 the products of adjacent cells, can you complete this Sudoku?