## Puzzle 10 (Hotaru Beam)

This is a Hotaru Beam puzzle.

Puzzle 10

I’m closer to working out how to make a good puzzle of this type. I managed to throw in more variety in this one, but I am a bit worried that too much “if-then” thinking is necessary.

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### 8 Responses to “Puzzle 10 (Hotaru Beam)”

1. Alan Curry Says:

This one doesn’t look good. I couldn’t make many logical deductions so I started randomly guessing and hit a solution really quick. And in several places, it’s flexible, suggesting a family of similar solutions. I’m too lazy to enumerate them all, but here’s a couple of them to demonstrate. Notice that even the long 20 beam has several places it could bend differently and still work.

2. MellowMelon Says:

Not the least bit surprised to hear this one was broken, considering how often I was goofing these up back then (before you were catching my errors, I was…), and how much trouble making these gave me. Hopefully fixed now.

• Alan Curry Says:

It’s impressive how fast you come up with fixes that maintain the difficulty of the puzzle. This was much more fun without all the guessing. A small flaw remains where the beam from one of the new circles can terminate in 2 different places, so there are still 2 solutions. I can see the easy fix too: put a number in that new circle.

3. MellowMelon Says:

Personally I think it’s more impressive that I can testsolve these multiple times and still leave this many screwups. Corrected.

4. rob Says:

Whew, did it, though I didn’t quite convincingly prove uniqueness there.

5. wartysoybean Says:

Was convinced of an error in the puzzle before reading the comments gave me doubts… finally found the solution, really tough finish for me to see. I think topological considerations go a long way in solving these Hotaru Beam puzzles.

6. xevs Says:

I used the Fact that I had noticed in puzzle 4 to solve this one. The Fact is… There is only 1 “loop” within a Hotaru Beam grid, that means, no second “loop”s can exist.

• MellowMelon Says:

Aha, so I was correct in my suspicion about what this fact you mentioned in 4 was. Yes, this was something I had noticed back in making these when I thought of this puzzle as being a graph, as all graphs with n vertices and n edges have exactly one cycle.