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2023-11-06 22:34 dustin  
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after four ΚΚΚΚs have broken "the unbreakable code" a few years ago, a new safe was created with a new code behind it. how many ΚΚΚs will be able to get the eight \\\ this time?

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2023-11-14 22:14 dustin  
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SOLUTION FREE! :D  
  
the synchronization of the ΠΠΠ is of course no coincidence, but it's based on the same pattern as in  altermaven 's cave "am23 256 peridot-b".   
  
the slime pattern is based on the following equation:  
  
f*s = 949-d  
  
where s is the total slime count in the cave, f and d are whole numbers, f is positive, while d can also be negative and should be between -s and s.  
  
if the equation is fulfilled, then the rule for the slime pattern goes:  
"whenever a specific Ι is permeable in a specific frame, then the d-th next Ι will be permeable f frames later."  
  
the ΙΙΙs are counted line by line, each line from left to right (cave-scanning order).  
  
this works because 949 is the cycle length of the rng used for ΙΙΙ, so all the permeable ΙΙΙ in my solution have the same rng value when they swallow their Π!  
  
the values in this cave are: s=116 f=8 d=21.  
  
the ΙΙΙs with a Π are always 8 rows away from each other, and there are always 20 other ΙΙΙs between them. that's why they can perfectly synchronize the ΠΠΠ!  
  
note that for any value of s, the equation is always fulfilled for some f and d values, although the result is usually not as striking. for example, in Κ's first ΙΙΙ cave, bd2-e, there's s=76 so the equation is true for f=12 and d=37. so the rule for bd2-e goes:  
"whenever a Ι in the first or second row is permeable, then the Ι which is two rows to the bottom and 1 column to the left will be permeable 12 frames later." (12 frames = 1-2 seconds depending on the difficulty level.)  
although i haven't checked it yet, it should be possible to notice that pattern in bd2-e, both in the original version and also in the version here at this site (although the slimes behaves differently, it still uses the same rng).  
  
in  altermaven 's aforementioned cave, with s=190, we have f=5 and d=-1. these low values make a very striking pattern - definitely check that one out! :d  
  
 nesdori : now i'm very curious if your solution is the same, or if you used different ΙΙΙs, or if you found a completely other way to solve the cave :d and, of course, if you found this one harder or easier than "the unbreakable code" :d

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2023-11-15 11:57 nesdori  
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my solution is the same. according to my calculations this is the only solution (assuming that 6+ sync falling ||| are needed; i'm not entirely sure if it's possible to sync drop more than 2| manually :)  
  
the whole cave Ι permeability cycle is 949 frames. so the cycle repeats in 949 frames / 8 fps = 118.6 secs. the are two occasions during the cycle when the solution Ι are permeable. the topmost solution Ι becomes permeable after 500 and 828 frames during a cycle. so the formula for solution Ι permeability moment is 500 + n * 949 cycles and 828 + n * 949 cycles which in game time means 62.6 secs + n * 118.6 secs and 103.5 secs + n * 118.6 secs. dirt must be present under each solution Ι when the previous permeable moment passes and then ^ must dig them free and position himself to do the manual sync drop by the next permeable moment.  
  
my solution uses the second permeable occasion of the 1st cycle,  dustin 's solution uses the first occasion of the 3rd cycle. that's why there's (949 - 828) + 949 + 500 = 1570 cycles = ~196 secs difference in our solutions. it's quite impossible to solve this using the first possible permeable moment after 62.6 secs; there's no enough time to do all the prerequisite digs and pushes.  
  
like "the unbreakable code 1", also this puzzle can be solved by cloning the cave, modifying it and then being observant. this might be actually be the simplest and fastest way to solve this cave. after cloning the cave, | should be placed on the top of each bottom Ι on each column. then all dirt from the uppermost magic wall to the bottom Ι on each column should be removed. then run the cave and place ^ near the topmost mw row and observe moments when multiple ||| fall in sync. because the cave is wider than ^'s viewport you should just look for left side first and then after potential partial sync fall also check the right side of the same moment. waiting on the left side, ^ sees that after 62.6 secs (+ the time the uppermost | needs to fall near mw) 5| fall in sync. then if the cave is rerun and ^ is placed on the right side he can see that additional | falls at the same on the right side. now the player has to realize that 6 sync ||| is enough to solve this cave because 2| can be sync-dropped manually, make notes about the columns where the sync ||| were falling and is then ready to actually solve the cave! :)

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2023-11-15 23:38 dustin  
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THANKS FOR PLAYING AND COMMENTING  nesdori ! :D  
  
actually, beside frames 500 and 828, there's also a third "permeable frame": 830, two frames after the second one. of course, that's not relevant for this cave:d  
  
if you make a 73x13 cave in the ckit, fill it completely with ΙΙΙ and show impermeable slimes, then you can see nicely that with permeability 8, there are three permeable frames inside a 949 cycle! and btw, if you set permeability 1, you get a very nice almost-symmetric picture of permeable and impermeable ΙΙΙs! :d  
  
i remember i once tried hard to sync-drop more than two ΒΒ w/o using any other elements for help, but i could sync-drop three ΒΒΒ only with help of open borders. i also made a cso cave of it :)

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2023-11-19 20:41 Arno  
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Great New episode to the slime permeability series, and very clear analysis! :-D

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2023-11-22 01:03 dustin  
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thanks  Arno ! :d i think thie phanomenon in this cave, as well as in  altermaven 's aforementioned cave, can be called a new section of the chapter "slime math" - after section 1 "impermeability", here we have section 2 "regular patterns"! especially with total ΙΙΙ counts close to 949, very striking patterns occur. i'm definitely going to make some more caves about that :d