L&D Fundamentals

The following problem was taken from the book Life and Death from the Elementary Go Series by Kiseido (page 59, problem 4). It has at least two solutions, but one is better than the other.

1st solution: Black lives with 3 points
2nd solution: Black lives with 4 points
It's pretty uncommon that once we find a solution to a problem, we keep on searching for better solutions. So this is to remind myself of that fact. Also, I realize that my search for a solution starts from the opposite direction, instead of first checking if closing the border works (which gives better follow up moves), I first try to make eyes from the "inside". This behavior is a pretty common pattern so that's why I wanted to point it out. And now that we're at it, why not remind ourselves the Fundamentals of Life and Death:

Life

1. Get more room (widen your eye space). 
2. Occupy a central eye making point (vital point). 

Death

1. Reduce the enemy's room (narrow his eye space). 
2. Occupy a central eye-making point.