## Maths challenge 1

Solve x² + y² + z² = 2xyz, where x,y,z are integers > 0 (i.e. natural numbers).

Addendum: In fact that isn’t possible to do. So I’ve ended up proving that

x² + y² + z² = 2n xyz cannot be solved for n,x,y,z in natural numbers.

Archive for April, 2011

Posted by Chris under MathsChallenge (32 Responds)

Solve x² + y² + z² = 2xyz, where x,y,z are integers > 0 (i.e. natural numbers).

Addendum: In fact that isn’t possible to do. So I’ve ended up proving that

x² + y² + z² = 2n xyz cannot be solved for n,x,y,z in natural numbers.

Posted by luv2fap under Tom (13 Responds)

An incredibly wealthy man offers you a 6 week job contract with his company. Being a generous man he also gives you choice as to how you will be paid: You can either get 1 million dollars each working day (Monday-Friday) for the entire 6 months OR he can start by paying you 1c on [...]

Tags: Maths Challenge
Posted by DP under Tom (25 Responds)

There is a room with 100 small un-locked safes numbered 1-100. A rich man places $1000 in each safe.

He then has 100 of his employees number off 1-100. He gives them keys to every ‘nth’ safe (n being the employee’s number), starting with thier number. (ex. employee 20 gets keys to safes 20, 40, 60, [...]

Posted by DP under Tom (25 Responds)

Can you prove that p^2 – 1 is always divisible by 24 for any prime number (p) greater than 3?

Posted by Karl Sharman under Tom (28 Responds)

London, Mid-day, Summer Equinox. Nelson’s Column. How much does it’s shadow weigh? Or perhaps the reverse is true? Does light somehow impose weight on an object, any object at all? The shadow weighs nothing… or less than nothing?

This comes from staring at the sun for too long!

Posted by Chris under MathsChallenge (16 Responds)

If m and n are positive integers and 33^m – 7^n = d, what is the smallest magnitude of d if d is positive and if d is negative? (That’s two questions).

100 mathematicians are challenged to a deadly game. There is a room into which there are 100 boxes numbered from 1 to 100, each of them containing the name of 1 of the 100 mathematicians. (so that each name is contained in a box, and we assume that no two mathematicians have the same name)

The [...]

Posted by Chris under MathsChallenge (15 Responds)

12 can be divided exactly by 6 numbers (including 1 and 12). How many numbers can 108 be divided by? What is the general formula?

By numbers, I mean positive integers.

This one’s pretty easy, and quite possibly useful.

Posted by Chris under MathsChallenge (16 Responds)

Evaluate Product((p² + 1)/(p² – 1)) where the product is over all the primes, p.

The answer is about 10% less than e.

The primes are: 2,3,5,7,11,13,…

I don’t know how to do it (but I haven’t really tried yet). It may require advanced mathematics (but I really don’t know if that’s the case). It was discovered by [...]