Planet Pather
Make paths between different planets with increasingly complicated rules across 35 levels. This puzzle game is a variant of the logic puzzle "hashiwokakero" (at least at first). There is a slight rule discovery element but most of the "difficulty" comes from the puzzles.
All of the puzzles in this game CAN be solved through pure logic (i.e. without guessing) and the puzzles in section 6 may require a pen and paper.
Made with PuzzleScript Next.
Original 8 minute OST made with Musescore by me. Truly one of the soundtracks of all time. There are two sound toggles, one for the music and one for the game sounds.
Comments
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Pretty fun, and I like the music!
I did 6-1 mostly and found a solution that works, but I'm having trouble proving its uniqueness. I know it had to be something related to the Section 5 mechanic, because otherwise I know it would not be unique, but I don't think I can find a satisfying way to prove it's impossible to get the others work. Any hint?
Proving that 6-1 has only one solution is a pretty difficult challenge. I've tried to put down into words how I proved this. Hopefully, it makes sense! I broke up my thinking into six steps. If you want to prove it yourself, only read down as far as you need to.
Explanation below (spoilers):
1. Even without considering limitations on movement, the "lying planet" can be narrowed down to either of the middle two planets in the second row (the green or brown).
2. Considering each planet as the liar individually, there are two solutions with a brown liar and only one with a green liar, for a total of three possible solutions. Now it needs to be proved that only one of these is possible. (In the following diagrams, an H is meant to be two vertical lines. The 3 is the green planet and the 6 is the brown planet).
~~Possibility 1~~
| H
=3 6
H
~~Possibility 2~~
| H
-3-6
|
~~Possibility 3~~
| H
-3=6
H
3. Horizontal and vertical movements are effectively separate in that a horizontal move will never change vertical lines, and vice versa. Only the vertical movement needs to be considered here.
4. The key is proving that the aforementioned brown planet (Row 2, Column 3) is limited to only connecting to the planet below it with one line, not two. If this is proved, only the second of the above possibilities would be valid.
5. It can be proved (by considering parity) that within the movement constraints and possible relative locations of the two astronauts in level 6-1, a single line, by itself, can never be created.
6. Given that (again, only considering the vertical lines) the puzzle CAN be solved using the second of the previous three possibilities, the other two must not be possible because the difference in vertical lines is exactly one line (below the lying brown planet).
(Un-ciphered spoilers after this)
Thanks for your reply. I got to step 4 on my own before making my first comment, and my intuition told me the exact thing I need to prove after that.
I did consider one form of parity, which is the numerical parity of horizontal/vertical lines. I thought the total number of either horizontal or vertical lines must be even because you must draw 2 lines per move, which could prove only one possibility works, but that's wrong because you can go from 2 to 0 by drawing "1 line", so I couldn't prove step 5 as easily as you have described.
But now that you mention it, I notice that there's also "positional parity", which allows me to color every (vertical) line with black or white, then notice you must draw 1 line in both black and white per move considering the relative positions of the astronauts. Drawing one line can cause the total number of lines go +1/-2 as mentioned before, and after all moves, the difference between black and white line numbers will always be a multiple of 3, finally proving that a difference of 1 in that other two possibilities can't ever happen.
I do feel satisfied with my proof no matter if it is the intended thought process or not, maybe there's an easier way to tell that? But if it is, I have to say you are evil LOL
I don't know how to solve the final level as logically. I feel that the combination of line-restriction and liar-rule seems it can only be solved by brute force.
And please make it possible to access all levels through level select. Even when I want to play only the last level, I had to start from the first level of that chapter again, which is not a good experiment.
I like the line-restriction, it’s a clever topology structure. But the liar-rule is really confusing, it’s difficult for me to find this fake planet.
The final level: In fact, it’s very clever. :D
This is really nice, the soundtrack is lovely too!
I’m stuck on chapter 4, would love a hint if someone has one 😅 Here’s my (incorrect?) understanding of the rule, in ROT13:
Bar bs gur cynargf vf n “yvne” naq jnagf bar zber be yrff guna vgf pbybhe jbhyq hfhnyyl fhttrfg - V qba’g xabj ubj gb gryy juvpu cynarg vf gur yvne gubhtu?
Glad you’re enjoying it!
I have two hints for you:
1. Lrf, bar bs gur cynargf vf n yvne, ohg abg arprffnevyl ol cyhf/zvahf bar. Gurzngvpnyyl, gur bhgre ynlre pnzr bss gur cynarg naq vf abj frra nebhaq gur obeqre bs gur chmmyr. Va frpgvbaf 5 naq 6, jura n chmmyr unf n obeqre, vg nyfb pbagnvaf n yvne.
2. Gur pbybhe bs gur chmmyr’f obeqre vaqvpngrf gur erny inyhr bs bar bs gur cynargf. Sbe rknzcyr, vs gur bhgre ynlre jnf terra, gura bar bs gur cynargf vf npghnyyl fhccbfrq gb or n guerr. Nf gb juvpu cynarg vf “ylvat,” vg vf hc gb lbh gb qrgrezvar.
nice game! gives a lot of hashi feels :)
for chapter 4 you should also show the color of the border, would be very convenient