## Puzzle 4 (Hotaru Beam)

This is a Hotaru Beam puzzle.

Puzzle 4

I had a lot of trouble with this. I like the concept of the puzzle, and I’ve thought of some neat things that can be done with it. But setting something clever up while making the solution unique and nontrivial to find is proving rather challenging. Hopefully I’ll be able to figure out how to do so eventually.

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### 8 Responses to “Puzzle 4 (Hotaru Beam)”

1. Alan Curry Says:

The Hotaru Beams are now the only puzzles here that I haven’t solved. Something’s wrong with this one, probably my understanding of the rules. Is it allowed to have a beam terminate at one of the “beam origin” dots, satisfying both circles with a single beam? If it’s allowed then the example solution wouldn’t be unique. On the other hand, I’ve tried solving this puzzle several times with the assumption that it’s not allowed, and every time I end up with the conclusion that there are no solutions.

• MellowMelon Says:

This puzzle has no solutions because I can’t count (fixed; the 5 was the problem). The beam can’t terminate at a beam origin dot because it can’t cross the beam coming out of the dot.

I haven’t really thought about these puzzles for awhile though. I can’t find a way to be clever with the rules and still leave a unique solution, so I’m hoping to find some that nikoli has put out at some point to figure out how to do them.

By the way, are these the only puzzle types you haven’t solved, or did you do all of the other 84? If the latter that’s pretty good; there are some really hard puzzles on here (although you got 21 and 50 and it’s downhill from there).

• Alan Curry Says:

Good, that 5 was the one causing me the most trouble. In the “beam terminates at a dot” case, I don’t see it as 2 beams crossing, I just see it as a single beam that satisfies 2 circles (which must have the same number if they are both numbered). The “single contiguous network” rule mentioned at Wikipedia was the last bit I needed to finish.

I’ve done 1 through 86 now, except for the second Hotaru Beam which I’ll do next.

2. David Says:

Hmmm, these are tough ones. The concept is good, and the puzzle itself is good, but Hotaru Beam puzzles just don’t seem very satisfying (thank god you only have two, and MathGrant doesn’t have any). Damn Nikoli.

3. John Reid Says:

Like Alan Curry, I was also at a standstill with this one until I used the ‘single contiguous network’ rule. I didn’t see any mention of that condition on your description page for this puzzle type – although the sample shown there would have more than one solution if you removed that restriction.

I haven’t seen one of these puzzles before. Interesting!

• rob Says:

Yes, the solution is not unique unless a single contiguous network is demanded. Without that rule, you can fill in all paths except for the one starting at (4,4) (numbered from (0,0) in NW), which could otherwise end in any of (3,2), (0,3), (2,5).

4. xevs Says:

I like solving way like this, and cute finishing! I noticed very important fact about this kind of puzzle after solving. I was lucky enough because this problem doesn’t require it.

• MellowMelon Says:

Interesting that this one was liked, as I thought it was among my weakest. I have an idea about this fact you noticed about the puzzle, and it may have been used in puzzle 10 (the only other Hotaru Beam I have posted).