@
xorsat
ahh yeah, I did eventually figure out that I had to click on the coloured tiles (I was clicking the greyed out ones, and it kept leading me to an interesting, but not solved, pattern). I think all thats missing is a little blurb saying to click the coloured tiles, though I think I was an outlier in being confused by that haha.
As for the ordering of inputs, there is a sort of "normal form" of any given board state that we can reach by moving all tiles (say, Light tiles for a Gloom board) to the bottom left. This process does change the solution, though, hence we leave the equivalence class and I hesitate to call it an honest-to-goodness normal form. After we move all tiles though, the solution your algorithm gives is the same one given by
this solver, which is interesting.
In fact, after doing a little bit of testing, the solution that your algorithm gives for the lower half of the board seems to be exactly the technique of moving everything down to the lower right corner. So long as I listen to the algorithm for the first 4-5 rows of hexes, then the solution remaining can be input by moving the remaining Light tiles to the lower right, akin to other people's solutions. By the time I'm clearing the middle row, I don't often need your algorithm to give me the solution anymore... quite interesting.
The hard part seems to come in choosing the correct moves on the upper half of the board so that the lower half is set up to be solved in that manner. I'm thinking it has something to do with the numbers and parity of Light hexes in each row, but I haven't noticed any strong patterns yet.
EDIT: also yeah, cynderfires probably has a good point here. Staff tend to not like anything interfacing with/reading the site iirc, hence the solver I linked being external and you have to input the boardstate yourself.
@
xorsat
ahh yeah, I did eventually figure out that I had to click on the coloured tiles (I was clicking the greyed out ones, and it kept leading me to an interesting, but not solved, pattern). I think all thats missing is a little blurb saying to click the coloured tiles, though I think I was an outlier in being confused by that haha.
As for the ordering of inputs, there is a sort of "normal form" of any given board state that we can reach by moving all tiles (say, Light tiles for a Gloom board) to the bottom left. This process does change the solution, though, hence we leave the equivalence class and I hesitate to call it an honest-to-goodness normal form. After we move all tiles though, the solution your algorithm gives is the same one given by
this solver, which is interesting.
In fact, after doing a little bit of testing, the solution that your algorithm gives for the lower half of the board seems to be exactly the technique of moving everything down to the lower right corner. So long as I listen to the algorithm for the first 4-5 rows of hexes, then the solution remaining can be input by moving the remaining Light tiles to the lower right, akin to other people's solutions. By the time I'm clearing the middle row, I don't often need your algorithm to give me the solution anymore... quite interesting.
The hard part seems to come in choosing the correct moves on the upper half of the board so that the lower half is set up to be solved in that manner. I'm thinking it has something to do with the numbers and parity of Light hexes in each row, but I haven't noticed any strong patterns yet.
EDIT: also yeah, cynderfires probably has a good point here. Staff tend to not like anything interfacing with/reading the site iirc, hence the solver I linked being external and you have to input the boardstate yourself.
i want to try this but my only browser is firefox... good job though, i don't understand most words here
i want to try this but my only browser is firefox... good job though, i don't understand most words here
@bubblegumwitch
[quote name="bubblegumwitch" date="2024-09-20 10:08:49" ]
Awesome - how applicable are these results to finding "biased"-minimal solutions for Glimmer exclusively or for Gloom exclusively? And are there any interesting findings about the relationship between Glimmer's and Gloom's biased-minimal solutions for a single puzzle?
E.g., does an even number of steps for Glimmer's biased-minimal solution imply anything about the evenness or oddness of Glimmer's biased-minimal solution?
[/quote]
I'm not sure; I haven't explored something like this yet. What I know is that often, the best solution for Glimmer has the same number of moves as the best solution for Gloom, but that's not always the case: sometimes a solution exists for Glimmer that is more minimal than the best solution for Gloom and vice versa. Whether or not in this case, Gloom's solution's has the same parity (evenness or oddness) as Glimmer's best solution, I'm not sure.
[quote name="bubblegumwitch" date="2024-09-20 10:08:49" ]
Also, and I'm not quite sure how to phrase this - what's the -jectivity situation between (non-redundant) solutions and boardstates? Which is to say, obviously you can reorder clicks, and obviously there's an infinite number of solutions in an equivalence-class for a given minimal solution (that is, it consists of that solution, plus any even number of additional clicks on any subset of the puzzle hexes). So we're setting aside permutations on a solution, and we're also setting aside solutions with purely-redundant clicks.
But, for a given board state, could there be a minimal solution for Glimmer that consists of four clicks, and ANOTHER solution for Glimmer that consists of six clicks, WITHOUT ever clicking the same hex twice?
[/quote]
In general, it depends on the "layout" of the board.
[LIST]
[*]For the easy game mode, the matrix [img]https://i.imgur.com/HNebkQO.png[/img] described in the post is full-rank (after Gaussian elimination, all columns are pivot columns). When considering solutions up to equivalence (combining solutions into the same class that preform unnecessary clicks or click the same tiles in a different order) there exists a unique solution for Glimmer, Gloom, or truly for any desired labeling.
[*]For medium, the matrix has rank deficiency 3, and since the free variables can take on any of two states (0 or 1), the number of distinct solutions is [img]https://i.imgur.com/wVjcEQz.png[/img] for any desired labeling.
[*] For hard, the matrix has rank deficiency 4, so there are [img]https://i.imgur.com/30fK2mI.png[/img] distinct solutions.
[*] For very hard, curiously, we're back to a full-rank matrix. There exists a single unique solution for any desired labeling.
[*] Special boards
[LIST]
[*] Four hexagons: the matrix has rank deficiency 10, so there are [img]https://i.imgur.com/kJfriRe.png[/img] distinct solutions
[*] For the dark symbol, the matrix has rank deficiency 1, so there are [img]https://i.imgur.com/LazQV6U.png[/img] distinct solutions
[*] For the light symbol, the matrix has rank deficiency 5, so there are [img]https://i.imgur.com/urCmPry.png[/img] distinct solutions
[*] For the flower, the matrix has rank deficiency 2, so there are [img]https://i.imgur.com/JBHvDLN.png[/img] distinct solutions
[/LIST]
[/LIST]
@
bubblegumwitch
bubblegumwitch wrote on 2024-09-20 10:08:49:
Awesome - how applicable are these results to finding "biased"-minimal solutions for Glimmer exclusively or for Gloom exclusively? And are there any interesting findings about the relationship between Glimmer's and Gloom's biased-minimal solutions for a single puzzle?
E.g., does an even number of steps for Glimmer's biased-minimal solution imply anything about the evenness or oddness of Glimmer's biased-minimal solution?
I'm not sure; I haven't explored something like this yet. What I know is that often, the best solution for Glimmer has the same number of moves as the best solution for Gloom, but that's not always the case: sometimes a solution exists for Glimmer that is more minimal than the best solution for Gloom and vice versa. Whether or not in this case, Gloom's solution's has the same parity (evenness or oddness) as Glimmer's best solution, I'm not sure.
bubblegumwitch wrote on 2024-09-20 10:08:49:
Also, and I'm not quite sure how to phrase this - what's the -jectivity situation between (non-redundant) solutions and boardstates? Which is to say, obviously you can reorder clicks, and obviously there's an infinite number of solutions in an equivalence-class for a given minimal solution (that is, it consists of that solution, plus any even number of additional clicks on any subset of the puzzle hexes). So we're setting aside permutations on a solution, and we're also setting aside solutions with purely-redundant clicks.
But, for a given board state, could there be a minimal solution for Glimmer that consists of four clicks, and ANOTHER solution for Glimmer that consists of six clicks, WITHOUT ever clicking the same hex twice?
In general, it depends on the "layout" of the board.
- For the easy game mode, the matrix
described in the post is full-rank (after Gaussian elimination, all columns are pivot columns). When considering solutions up to equivalence (combining solutions into the same class that preform unnecessary clicks or click the same tiles in a different order) there exists a unique solution for Glimmer, Gloom, or truly for any desired labeling.
- For medium, the matrix has rank deficiency 3, and since the free variables can take on any of two states (0 or 1), the number of distinct solutions is
for any desired labeling.
- For hard, the matrix has rank deficiency 4, so there are
distinct solutions.
- For very hard, curiously, we're back to a full-rank matrix. There exists a single unique solution for any desired labeling.
- Special boards
- Four hexagons: the matrix has rank deficiency 10, so there are
distinct solutions
- For the dark symbol, the matrix has rank deficiency 1, so there are
distinct solutions
- For the light symbol, the matrix has rank deficiency 5, so there are
distinct solutions
- For the flower, the matrix has rank deficiency 2, so there are
distinct solutions
[quote name="Cynderfires" date="2024-09-20 15:04:59" ]
I think this type of extension might not be allowed- I'd double check with a staff member before using it
[/quote]
[quote name="Lumen" date="2024-09-20 15:05:48" ]
EDIT: also yeah, cynderfires probably has a good point here. Staff tend to not like anything interfacing with/reading the site iirc, hence the solver I linked being external and you have to input the boardstate yourself.
[/quote]
@Cynderfires @Lumen
Good points. I've submitted a ticket to the staff (#88153 if a staff member is reading this) to see what they say. I'm hoping they're cool with it. Happy to make changes if necessary.
Cynderfires wrote on 2024-09-20 15:04:59:
I think this type of extension might not be allowed- I'd double check with a staff member before using it
Lumen wrote on 2024-09-20 15:05:48:
EDIT: also yeah, cynderfires probably has a good point here. Staff tend to not like anything interfacing with/reading the site iirc, hence the solver I linked being external and you have to input the boardstate yourself.
@
Cynderfires @
Lumen
Good points. I've submitted a ticket to the staff (#88153 if a staff member is reading this) to see what they say. I'm hoping they're cool with it. Happy to make changes if necessary.
@Lumen
[quote name="Lumen" date="2024-09-20 15:05:48" ]
I think all thats missing is a little blurb saying to click the coloured tiles, though I think I was an outlier in being confused by that haha.
[/quote]
This is good feedback! Maybe something simple like that blurb would clear up any confusion.
[quote name="Lumen" date="2024-09-20 15:05:48" ]
As for the ordering of inputs, there is a sort of "normal form" of any given board state that we can reach by moving all tiles (say, Light tiles for a Gloom board) to the bottom left. This process does change the solution, though, hence we leave the equivalence class and I hesitate to call it an honest-to-goodness normal form. After we move all tiles though, the solution your algorithm gives is the same one given by this solver, which is interesting.
[/quote]
One point about this I think is important to mention is that the way the tool currently works, it doesn't re-compute the minimal solution every time you update the game. Instead, it solves it once and "remembers" that specific solution. That way if you mess up and click something you weren't supposed to, it'll just highlight the one tile you accidentally clicked in addition to the original set of tiles from the minimal solution. You can force the tool to re-compute the minimal solution by switching to light (assuming you were on dark) and back again. In the few examples I tested where I started off by ignoring the tool's solution and just did a normal "light chasing" run until I moved everything into the bottom-right, forcing the tool to compute a new solution didn't actually make a difference, but I don't know if that's true in general. Just something to be aware of.
[quote name="Lumen" date="2024-09-20 15:05:48" ]
In fact, after doing a little bit of testing, the solution that your algorithm gives for the lower half of the board seems to be exactly the technique of moving everything down to the lower right corner. So long as I listen to the algorithm for the first 4-5 rows of hexes, then the solution remaining can be input by moving the remaining Light tiles to the lower right, akin to other people's solutions. By the time I'm clearing the middle row, I don't often need your algorithm to give me the solution anymore... quite interesting.
The hard part seems to come in choosing the correct moves on the upper half of the board so that the lower half is set up to be solved in that manner. I'm thinking it has something to do with the numbers and parity of Light hexes in each row, but I haven't noticed any strong patterns yet.
[/quote]
I'm exactly where you're at: I more-or-less trust the tool for the upper half of the game (including the middle row), but then after that I can just do the normal "light chasing" strategy by moving everything to the right and it works out and the game is solved. I've played around with trying to figure out patterns in the top half solutions, but haven't figured out anything super useful.
I thought I was onto something where I tried this approach
[LIST=1]
[*]Trust the solution given by the tool for just the first row
[*]Starting with the second row and up to and including the middle row, clear the light tiles (I almost always play for Gloom) row-by-row in the fewest number of moves I can, by "moving" some to the left and some to the right.
[*]For the remaining rows, just do "light chasing" by moving everything to the right.
[/LIST]
What I found is that this kinda works sometimes, but not for every board: even if I perform what I think is the fewest number of moves for a given row in that upper half, I can end up in a situation where a single light-chasing pass of the board isn't sufficient and I end up with light tiles in the bottom-right edges of the board. But I'm hopeful that a more friendly-to-humans approach exists where folks can find a minimal solution without referring to the tool.
Edit 9/25/2024:
I realized that for the hexagonal game modes (medium/hard/very hard) you can actually just use the tool for figuring out which tiles in the top row and the upper-left diagonal to click. After you've done that, you can just do the normal "light chasing" strategy: for each light tile, click the tile to its bottom-right. If you do that, you'll end up solving the puzzle.
@
Lumen
Lumen wrote on 2024-09-20 15:05:48:
I think all thats missing is a little blurb saying to click the coloured tiles, though I think I was an outlier in being confused by that haha.
This is good feedback! Maybe something simple like that blurb would clear up any confusion.
Lumen wrote on 2024-09-20 15:05:48:
As for the ordering of inputs, there is a sort of "normal form" of any given board state that we can reach by moving all tiles (say, Light tiles for a Gloom board) to the bottom left. This process does change the solution, though, hence we leave the equivalence class and I hesitate to call it an honest-to-goodness normal form. After we move all tiles though, the solution your algorithm gives is the same one given by this solver, which is interesting.
One point about this I think is important to mention is that the way the tool currently works, it doesn't re-compute the minimal solution every time you update the game. Instead, it solves it once and "remembers" that specific solution. That way if you mess up and click something you weren't supposed to, it'll just highlight the one tile you accidentally clicked in addition to the original set of tiles from the minimal solution. You can force the tool to re-compute the minimal solution by switching to light (assuming you were on dark) and back again. In the few examples I tested where I started off by ignoring the tool's solution and just did a normal "light chasing" run until I moved everything into the bottom-right, forcing the tool to compute a new solution didn't actually make a difference, but I don't know if that's true in general. Just something to be aware of.
Lumen wrote on 2024-09-20 15:05:48:
In fact, after doing a little bit of testing, the solution that your algorithm gives for the lower half of the board seems to be exactly the technique of moving everything down to the lower right corner. So long as I listen to the algorithm for the first 4-5 rows of hexes, then the solution remaining can be input by moving the remaining Light tiles to the lower right, akin to other people's solutions. By the time I'm clearing the middle row, I don't often need your algorithm to give me the solution anymore... quite interesting.
The hard part seems to come in choosing the correct moves on the upper half of the board so that the lower half is set up to be solved in that manner. I'm thinking it has something to do with the numbers and parity of Light hexes in each row, but I haven't noticed any strong patterns yet.
I'm exactly where you're at: I more-or-less trust the tool for the upper half of the game (including the middle row), but then after that I can just do the normal "light chasing" strategy by moving everything to the right and it works out and the game is solved. I've played around with trying to figure out patterns in the top half solutions, but haven't figured out anything super useful.
I thought I was onto something where I tried this approach
- Trust the solution given by the tool for just the first row
- Starting with the second row and up to and including the middle row, clear the light tiles (I almost always play for Gloom) row-by-row in the fewest number of moves I can, by "moving" some to the left and some to the right.
- For the remaining rows, just do "light chasing" by moving everything to the right.
What I found is that this kinda works sometimes, but not for every board: even if I perform what I think is the fewest number of moves for a given row in that upper half, I can end up in a situation where a single light-chasing pass of the board isn't sufficient and I end up with light tiles in the bottom-right edges of the board. But I'm hopeful that a more friendly-to-humans approach exists where folks can find a minimal solution without referring to the tool.
Edit 9/25/2024:
I realized that for the hexagonal game modes (medium/hard/very hard) you can actually just use the tool for figuring out which tiles in the top row and the upper-left diagonal to click. After you've done that, you can just do the normal "light chasing" strategy: for each light tile, click the tile to its bottom-right. If you do that, you'll end up solving the puzzle.
[quote name="akesi" date="2024-09-20 16:24:40" ]
i want to try this but my only browser is firefox... good job though, i don't understand most words here
[/quote]
@akesi
I'll hold off until at least I get a response back from the staff that the extension is okay. But yeah, my own choice of browser is also Firefox, so I might end up porting it to work there as well.
akesi wrote on 2024-09-20 16:24:40:
i want to try this but my only browser is firefox... good job though, i don't understand most words here
@
akesi
I'll hold off until at least I get a response back from the staff that the extension is okay. But yeah, my own choice of browser is also Firefox, so I might end up porting it to work there as well.
Thank you so much for this!! I really was struggling with this game and I'm happy to have help now.
Edit: I do want to say it's working perfectly and I really like the very simple design of it.
Thank you so much for this!! I really was struggling with this game and I'm happy to have help now.
Edit: I do want to say it's working perfectly and I really like the very simple design of it.
this is super super cool!! amazing work!! if staff end up approving this, my only suggestion would be an option to make the background of the window darker - its a little difficult to figure out where the edges of the guide board is :]
this is super super cool!! amazing work!! if staff end up approving this, my only suggestion would be an option to make the background of the window darker - its a little difficult to figure out where the edges of the guide board is :]
|
HUNTER / HARVEY
any prns / +8 fr time
|
|
[quote name="giraffesonparade" date="2024-09-22 17:03:18" ]
Thank you so much for this!! I really was struggling with this game and I'm happy to have help now.
Edit: I do want to say it's working perfectly and I really like the very simple design of it.
[/quote]
@giraffesonparade I'm so happy that it's helpful! I'm gonna try to make sure it stays simple!
giraffesonparade wrote on 2024-09-22 17:03:18:
Thank you so much for this!! I really was struggling with this game and I'm happy to have help now.
Edit: I do want to say it's working perfectly and I really like the very simple design of it.
@
giraffesonparade I'm so happy that it's helpful! I'm gonna try to make sure it stays simple!
[quote name="R3VOLUTIONN" date="2024-09-24 01:42:43" ]
this is super super cool!! amazing work!! if staff end up approving this, my only suggestion would be an option to make the background of the window darker - its a little difficult to figure out where the edges of the guide board is :]
[/quote]
@R3VOLUTIONN That's great feedback! In retrospect, maybe light-gray-on-white wasn't a great choice haha
R3VOLUTIONN wrote on 2024-09-24 01:42:43:
this is super super cool!! amazing work!! if staff end up approving this, my only suggestion would be an option to make the background of the window darker - its a little difficult to figure out where the edges of the guide board is :]
@
R3VOLUTIONN That's great feedback! In retrospect, maybe light-gray-on-white wasn't a great choice haha
