Puzzle time - don't waste braindead liberals

[Klaus]

Assume Larry and Ax are at a fixed position in a large rectangular room with mirrors as walls. Ax is trying to attack Larry with a laser, potentially using the mirrors to reflect the laser beam (the laser can bounce arbitrarily many times). But Larry is so lucky to have a couple of disposable braindead liberals that he can place arbitrarily in the room to block a potential shot. So the situation looks something like this (for some arbitrary positions):

Larry has to place the braindead liberals before Ax aims and shoots. How many braindead liberals would Larry need to be safe, regardless of the direction in which Ax shoots, and where would they need to be placed? We all know that braindead liberals are not well fed, so we assume that they only occupy a mathematical point of space. Also, Larry has to be shot precisely in the center, so we can also assume that he only occupies a mathematical point.

[jon-nyc]

So Ax’s position is known to Larry before he places his BDLs? And Ax can’t subsequently move?

[Klaus]

Yes, both are at a fixed position.

[Doctor Phibes]

Can't we just throw a hand grenade into the room and be done with it?

[Klaus]

Here's an important intermediate steps to consider:

Show that you don't need "continuum" many BDLs (e.g., to form a circle around Larry) but can get by with countably many BDLs (still potentially infinitely many, but at least you can count them).

The puzzle can be solved with a finite number of BDLs, but the above intermediate step isn't trivial.

[Klaus]

For those who need an additional big hint. Don't look if you want the full fun

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Here's an example of how to place BDLs - in this case 16 - that will prevent any attack, regardless of how many bounces. One possible attack with two bounces is indicated in the drawing. The coordinates of the BDLs as well as Ax and Larry can also be seen. Try it out. It's a safe position for Larry.

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[George K]

@Klaus , you and @jon-nyc need to get a room.

SRSLY

[taiwan_girl]

Have to think more, but it seems like it would be a large number. Just thinking out loud, if Ax shoots almost horizontal, but a small angle less than that, the back and forth an infinite number of times.

Anyway, have to think more. (But still probably won't be able to discover the answer 55555)

[Larry]

I wouldn't need to move. I'd simply stare at him and tell him if he moves an inch I'm going to break the rules and go over and slap him into next week, and he would shit himself and pass out.

Then I'd come looking for the guy who put me in a room with Ax.

[Doctor Phibes]

@George-K said in Puzzle time - don't waste braindead liberals:

@Klaus , you and @jon-nyc need to get a room.

SRSLY

Preferably one with big fuckoff lasers in it.

[jon-nyc]

Don’t post an answer yet I want to play with this tonight.

[LuFins Dad]

Are the brain dead liberals the same size as Larry? They’re likely vegan, and tiny little things...

[Klaus]

Indeed. So tiny that they have no extension.

[jon-nyc]

Does Larry have to worry about shooting himself?

[jon-nyc]

I’m guessing it’s a countably infinite answer that is related to the primes but I still need to work on it.

[Klaus]

No, it's a very finite number.

[jon-nyc]

Ok. I think I can see that now... more tomorrow

[Klaus]

This puzzle can be solved using high school math and geometry knowledge. Actually, basically no math/geometry is involved apart from knowing how a mirror reflects a laser (incoming angle = outgoing angle).

I can add a few more hints if it is too hard (well, it is hard).

[jon-nyc]

Don’t add any hints

[bachophile]

Link to video