Project Euler Forum

In problem 202 what happens if the beam hits a vertex other than the exit one, or is that not allowed? I can't see it being explicitly disallowed in the statement.

... and if it's allowed does it bounce in the direction symmetric to the bisectrix of the angle, and does it count as having bounced off of 0, 1 or 2 surfaces?

If the beam hits a vertex, it exits the chamber.

Ooops. Understood.

Am I correct in guessing that there are 2 ways for such a path to hit 7 (and for 13) surfaces?

You shouldn't guess that but count or calculate it , but the numbers are correct.

actually, I wasn't guessing...
so now I have 2 pieces of the problem..now for the third!

Does anybody have a quantum computer to lend me?

sfabriz wrote:Does anybody have a quantum computer to lend me?

I do use one for some other problems... estimated duration is still three times the age of the universe. You'll have to wait a bit

Tommy137 wrote:I do use one for some other problems... estimated duration is still three times the age of the universe. You'll have to wait a bit

D'oh!

Don't worry, just hack into the supercomputer in "A Hitchhiker's Guide to the Galaxy" and it'll take a few thousand years...
OR hack into the Earth itself, and it'll be done in 2 seconds...

I'm having an incredibly difficult time building an intuition on problem 202. I don't seem to be able to mentally trace laser beams for enough bounces to get more than the one distinct path to exit (not including the uninteresting reverse path). I've figured out some interesting properties on how the beams bounce around, but I fear that I'll never make the final connection until I can precisely visualize more interesting cases.

I don't want someone to give me a hint on how to discover these interesting cases. I want some suggestions for simple, lightweight programming languages that will let me quickly create something that will draw out the paths of a laser bouncing off mirrors (similar to the picture in the problem description). I could do it with openGL connectors, but that's complete overkill, so I'd like to use this as an opportunity to learn a new tool.

Any popular suggestions? (Remember, I definitely don't want hints about the problem. I mention it only to demonstrate what kind of simple functionality I need.)

I made a little program in Maple to draw the paths depending on the incoming angle. Maple allows you to draw linesegments by specifying the endpoints coordinates. There are probably a lot of other programs that can do this too

It didn't help any at all though ..

I wish I still had free access to Maple and especially Mathematica. There ought to be a "harmless math geek" license for ex-students who want to play around but aren't doing anything productive enough to justify the extreme license costs. Maybe I need to look deeper into Sage.

It didn't help any at all though ..

*sigh* I'm still going to write my program (in Visual C#, for now). Hopefully I'll be able to create just one example of multiple distinct paths with the same number of reflections.

This problem taunts me like no other. So many people (relatively speaking) have solved it, but I can't even get in the front door. Small examples exist to be generated, but every time I try to sketch one I mess up. It's maddening, and I don't think my mind will ever be at rest until it clicks.

Does it count as a clue to say I had to draw it on paper before it finally clicked? I hope not. Very very deceptive problem. Actually experimenting & trying to find an angle that did those reflections didn't do a lick of help for me.

quilan wrote:Does it count as a clue to say I had to draw it on paper before it finally clicked? I hope not. Very very deceptive problem. Actually experimenting & trying to find an angle that did those reflections didn't do a lick of help for me.

This is good advice. The diagram given with the problem is (intentionally?) useless. If you can redraw it so that you can solve the warmup problem you are on your way to a programmed solution.

 
As its creator, I can tell you that the diagram's uselessness was totally unintentional
(I used R, btw)
 

Done! And this completes my interim goal of solving the twenty-five most recent problems. Man, I haven't been this satisfied in a while.

(I used R, btw)

Thanks, although I tripped over other means of understanding this problem, it looks like an interesting tool.

Yus, I hope my non-clue helped some .

It helped me not dispair when I couldn't make heads or tails of the output of the crappy drawing program I stubbornly wrote. So, thanks.