The Three Point Conjecture

Don't get too excited about the title. It's simply a puzzle(The three utilities puzzle).

There are three houses and three factories(water,gas,electricity) in a city block.Each house should be supplied with water,gas and electricity.The supply lines should not overlap each other.Draw the connections.

In short there are 2 sets of three points.Each point in Set-1 should be connected to every point in Set-2 without the lines overlapping.

Seems easy enough.But there's a catch, no matter how you try, you won't be able to make one last connection.You don't want to know how much time I spend on it and was convinced of its impossibility.

Now one last challenge remained - the proof.
The difficult part about the proof was that I've got no idea where to begin or which path to follow.Proving something like this was entirely new. It disturbed me day and night. It's amazing how desperation could make you do things that you thought you couldn't. And this fine morning something strange struck me.

Balancing Chemical Equations [LifeHack]

Its not often that we come across chemical equations with coefficients like 48 and 50.But when we do most of us are meant to screw up.Thats exactly why a friend of mine asked me to come up with something.(Its hard enough just to memorise all those equations.)

I'll show you how to balance complicated chemical equations with huge coefficients easily and quickly.All you need to know is how to solve linear equations in variables.

The method might seem long but the equations that we get are simple and the method is much quicker than manually trying to balance the atoms.

Steps: 

1.Assign coefficients to each term in the equation (a,b,c.....)

2.Now balance each element i.e. solve for the coefficients.

(You can skip some steps by assigning coefficients directly as shown below)

Lets start with..

S₈ + HNO₃ = H₂SO₄ + NO₂ + H₂O