8 ms·

This was beautiful. I never imagined the existence of a solution was always guaranteed, given that this includes the case where you are using point-particle blo

• uuidgen 5y ago
  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
  • zzt123 5y ago
    This line of reasoning reminds me of that one IMO geometry problem… I’ll unwind this once I’m less brain foggy.