Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

voider

Member Since --
Offline Last Active Jul 04 2012 06:07 AM
-----

Topics I've Started

09 November 2011 - 07:09 AM

If you have 7 integer variables, e.g. a, b, c, d, e, f, g, and you can use each at most once in an expression with the operators +, -, *, / (integer division), how many unique expressions can be formed?
E.g. (a - b) * c + f is mathematically the same as:
c * (a - b) + f
f + (a - b) * c
f + c * (a - b)
so they all correspond to a single unique expression.

If there was one variable, there are 7 unique expressions.
With two variables, I think there are 133 unique expressions.

I don't know the answer (yet), and I very much doubt anyone can find a closed form formula for the general problem. About the context where this problem originated, I suspect it was intended to be virtually unsolvable... :) (and deceptively mediocre-looking)