I think the solution can be reached following from a set of simple observations about a single line of sight:
- in a square room all angles are right
- with wall at right angles the laser light will always create an inscribed square and return to the source for any given angle
- there is exactly one angle in a range <0,90> at which the light bounced from a single wall will go through an arbitrary point in the room
- there are 4 walls which gives at most 4 squares to be blocked
- the blocking point can be set anywhere on the inscribed square before the target - this gives at most 2 points per square (we can consider them left- and right- -hand directed) hence 8 points necessary
- at start we selected only angles from the <0,90> degree range for the ease of calculation, so there are also symmetric versions in the (90,180> range
- which gives us at most 16 points to block all the possible squares in both directions
- in a square room all angles are right
- with wall at right angles the laser light will always create an inscribed square and return to the source for any given angle
- there is exactly one angle in a range <0,90> at which the light bounced from a single wall will go through an arbitrary point in the room
- there are 4 walls which gives at most 4 squares to be blocked
- the blocking point can be set anywhere on the inscribed square before the target - this gives at most 2 points per square (we can consider them left- and right- -hand directed) hence 8 points necessary
- at start we selected only angles from the <0,90> degree range for the ease of calculation, so there are also symmetric versions in the (90,180> range
- which gives us at most 16 points to block all the possible squares in both directions