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dustin's bd25 cave p l5
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by
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dustin
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DUSTIN                            2025-11-03 10:53
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AND HERE COMES THE BIG FINAL! WITH 111Α REQUIRED, Κ HAS TO DIG A VERY EFFICIENT, TIME-CONSUMING PATH FOR THE Ζ.   
  
I'M STILL WONDERING WHAT THE BEST POSSIBLE PATH WOULD BE, SUCH THAT THE Ζ TAKES AS MUCH TIME AS POSSIBLE. WHEN I TESTED THIS CAVE BEFORE THE RELEASE, I TRIED DIFFERENT VARIANTS, AND MY BEST ONE GOT ME 117Α.   
  
SO I RELEASED THE GAME WITH THE STILL OPEN QUESTION IF IT'S POSSIBLE TO GET ALL THE 120Α AVAILABLE! (AND IF IT IS POSSIBLE, THEN HOW MANY MORE ΑΑΑ WOULD BE POSSIBLE IF THE ΑΑΑ ROW CONTINUED?)  
  
WELL, I GUESS IT'S ALREADY TRICKY ENOUGH TO GET THE REQUIRED 111Α! THE BEST (VISIBLE) RUN ON LEVEL 1 GOT "ONLY" 106Α, SO THAT STILL NEEDS IMPROVEMENT!)  
  
DIFFICULTY: 7/10 (117Α: 9/10, 120Α: NOT SURE IF POSSIBLE)

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DARKSTOORM                        2025-11-03 23:57
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I CAN ONLY GET 116 :D

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HEYWOOD                           2025-11-04 03:18
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"ONLY" :D

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NESDORI                           2025-11-04 21:37
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I GOT 199Α WITH FOUR SLIGHTLY DIFFERENT TRIES. IT TAKES 2 FRAMES IMPROVEMENT TO GET ADDITIONAL Α AND ALL THOSE WERE EXACTLY THE SAME "LOW" 199Α WITH 2 FRAMES AWAY FROM 200Α AND NOT "HIGH" 199Α WITH JUST ONE FRAME AWAY.  
  
IT SEEMS THAT THERE'S FINE BALANCE BETWEEN DIFFERENT MEANS TO MAXIMIZE THE TIME THE FLY SPENDS ON THE LEFT SECTION. THOSE MEANS INCLUDE MAXIMIZING THE PATH LENGTH, MAXIMIZE THE NUMBER OF LOCATIONS WHERE THE FLY VISITS 3-4 TIMES (INTERSECTIONS) AND MAXIMIZE THE TURNS THE FLY HAS TO MAKE (AND AVOID STRAIGHT PATHWAYS). IF YOU WEIGHT ONE THOSE, THE TWO OTHER SUFFER. AND NO MATTER HOW I TRIED TO WEIGHT THEM THE BEST RESULT IS ALWAYS 199Α ALTHOUGH THE SOLUTIONS LOOK A BIT DIFFERENT.   
  
BECAUSE THERE HAVE BEEN SO MANY 199Α:S, MOST PROBABLY I HAVE MISSED SOMETHING SOMETIMES AND AT LEAST HIGH 199Α WITH ONE FRAME IMPROVEMENT SHOULD BE POSSIBLE. MAYBE EVEN 2 FRAMES ALTHOUGH CURRENTLY IT FEELS QUITE IMPOSSIBLE.  
  
UPDATE TO dustin'S DIFFICULTY RATINGS:  
  
199Α, 9.5/10  
200Α, STILL NOT SURE IF POSSIBLE :)

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NESDORI                           2025-11-04 21:48
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OF COURSE 119Α AND NOT 199Α :D

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DARKSTOORM                        2025-11-04 22:44
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THIS MAKES ME THINK THAT MAYBE SOME "MAZE GENERATOR" FOR FIREFLY WOULD BE IN PLACE THAT WOULD SEARCH FOR THE LONGEST POSSIBLE PATH IN THIS SETTING, MAYBE IT COULD FIND 120+! :D

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NESDORI                           2025-11-04 23:10
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darkstoorm, INTERESTING IDEA BUT I THINK IT WOULD BE A TOUGH CHALLENGE FOR COMPUTERS AND AI TO BEAT HUMAN MIND HERE IN SENSIBLE TIME. IT'S NOT ONLY ABOUT THE MAZE ITSELF BUT ALSO ABOUT Κ PASSING THE FLY. BUT MAYBE DOABLE IF THE INPUT ALREADY IS 119Α SOLUTION AND THE TASK IS JUST TO IMPROVE THAT.. :) WHAT I FOUND DIFFICULT IS THAT SOMETIMES I ENDED UP WITH CLOSED SECTIONS AND THEN DECIDING HOW TO CONNECT EACH SECTION EFFECTIVELY WAS QUITE CHALLENGING AT TIMES.

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DUSTIN                            2025-11-05 13:28
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HEEEY, nesdori, GOOD TO SEE YOU AGAIN AFTER SEVERAL MONTHS! :)  
  
IN FACT, I WAS ACTUALLY KINDA HOPING THAT YOU'D COMMENT ON THIS TOPIC, I THINK SUCH "PATH MAXIMIZING" TASKS COULD BE AN INTERESTING TOPIC FOR FURTHER CAVES :D  
  
darkstoorm, INTERESTING IDEA TO DO ANOTHER BRUTE FORCE SEARCH WITH COMPUTERS AFTER THE WHOLE DFF SEARCH! MAYBE IT WOULD MAKE SENSE TO START WITH SMALLER 'BOARDS' THAN 11X11, SUCH THAT THE BRUTE FORCE STILL ENDS BEFORE STAR TREK BEGINS :D THEN WE COULD SEE IF WE DISCOVER PATTERNS WHICH CAN ALSO BE USED FOR BIGGER BOARDS!

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DARKSTOORM                        2025-11-06 01:33
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dustin, nesdori: I'M GONNA TAKE A WILD GUESS, MAYBE A GENETIC ALGORITHM WOULD DO THE TRICK? NEVER TRIED IT, THOUGH :D  
  
NOT SURE I WANT TO ATTEMPT THIS, THE ONLY THING I TRIED FOR NOW WAS JUST PRINTING THE Ζ PATH LENGTH FROM A CAVE SETUP, PLACING RANDOMLY DIRT/SPACE AND CHECKING WHICH ONE IS THE LONGEST (ONLY MANUALLY, THOUGH).  
  
I DIDN'T HAVE MUCH TIME TO TEST THIS, BUT I ASSUME THE Ζ HAS TO BE SCANNED AT LEAST:  
- 239 TIMES (YOU SNAP THE LAST Α)  
- + WHATEVER IT TAKES ^ TO GET TO THE FIRST Α, WHICH I THINK IS 7 IF Ζ IS TO THE LEFT OF THE Ε CORNER  
- + I THINK 2 TO ALLOW ^ TO GO UP WITHOUT GETTING TOUCHED (Ζ HAS TO BE 2 CELLS TO THE LEFT WHEN REACHING THE ENTRANCE)  
- +1 MORE MOVE TO REACH THE ENTRANCE ABOVE ^ (FIRST DIAMOND IS ONE CELL TO THE RIGHT OF THE ENTRANCE ABOVE)  
  
I MIGHT HAVE MISSED SOMETHING, BECAUSE THIS GIVES 249 SCANS AND DEPENDING ON WHERE WE START MEASURING, MY GUESS IS THAT Ζ HAS TO BE SCANNED AROUND 254 TIMES FOR A 120Α RUN, ASSUMING THE FOLLOWING STARTING SETTING:  
  
^.....Α GONNA MISS ONE FRAME HERE NO MATTER WHAT;  
.ΖΕΕΕΕΕ Ζ HAS TO BE SCANNED  
  
NO CLUE YET, BUT I'D LOVE TO SEE A FULL RUN!

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NESDORI                           2025-11-07 02:21
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darkstoorm, INTERESTING THOUGHTS! WHEN IT'S TIME TO REVEAL THE SOLUTIONS, I'LL SHOW TWO DIFFERENT 119Α SOLUTIONS WITH EMPHASIS ON DIFFERENT THINGS WHICH MIGHT GIVE YOU EVEN MORE IDEAS :)

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DUSTIN                            2025-11-09 20:37
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darkstoorm, nesdori: I REFRAINED FROM ANSWERING UNTIL NOW BECAUSE I CONSIDER MYSELF ONE OF THE MOST PROGRAMMING-NOOB PHYSICIANS IN THE WORLD, AND I ALREADY STUMBLED OVER THE TERM "GENETIC ALGORITHM", ALTHOUGH NOW THAT I READ A BIT ABOUT IT IT SOUNDS VERY COOL :D  
  
HERE ARE MY THOUGHTS:  
  
| ABOUT darkstoorm'S COUNTING: I THINK THE Ζ HAS TO SPEND 245 FRAMES INSIDE THE 11X11 BOX (FOR A 120Α RUN TO WORK):  
- 8 FRAMES UNTIL Κ IS IN FRONT OF THE FIRST Α (IN THE SITUATION SHOWN IN darkstoorm'S COMMENT, THE Ζ IS ALREADY 2 FRAMES IN, NOW Κ MUST WAIT ONE MORE FRAME AND THEN MOVE 5 FRAMES);  
- 120 FRAMES TO TAKE THE ΑΑΑ, SNAPPING THE LAST ONE;  
- AND 119 FRAMES BACK, FROM WHERE HE CAN GO UPWARDS TO THE Β TO CRUSH THE Ζ.  
- AT THAT POINT, THE Ζ IS IDEALLY 2 LEFT FROM Κ, WHICH MEANS IT'S ALREADY TWO FRAMES OUT OF THE BOX AGAIN.  
SO THAT MAKES 8+120+119-2 = 245 FRAMES INSIDE THE BOX.  
  
| THOUGHTS ON HOW TO EVALUATE POSSIBLE PATH CONSTRUCTIONS:  
  
FOR THE FOLLOWING, A "LOOP" IS A SPACE ARRANGEMENT FORMING A CLOSED CIRCLE, SO THAT A Ζ (OR Η) COULD BE PLACED SOMEWHERE ON THE LOOP AND, WITH SOME INITIAL DIRECTION, STAY INSIDE THE LOOP FOREVER. (JUST THE INTUITIVE DEFINITION FOR A BOULDER DASHER, I GUESS!)  
  
I ASSUME (BY FEEL, FOR NOW) THAT PATHS WITHOUT ANY LOOPS ARE BETTER THAN PATHS WITH LOOPS, SO I CONSIDER ONLY PATHS CONTAINING NO LOOPS AT ALL.  
  
BESIDES, A "PATH" IS AN ARRANGEMENT OF EMPTY SPACE IN THE 11X11 BOX WHERE EVERY SPACE IS CONNECTED TO EVERY OTHER. (OTHERWISE IT'S CLEARLY NOT THE OPTIMUM.)  
  
ON A LOOP-LESS PATH, IT SHOULD BE POSSIBLE TO EASILY VALUE EACH EMPTY SPACE WITH A NUMBER THAT SAYS HOW MANY FRAMES THE Ζ WILL BE THERE IN TOTAL:  
Α VALUE 4 IF THE SPACE IS CONNECTED TO FOUR OTHER SPACES IN EACH DIRECTION (THE Ζ WILL RETURN FOUR TIMES FOR ONE FRAME EACH);  
Α VALUE 3 IF THE SPACE IS CONNECTED TO EXACTLY THREE OTHER SPACES (SIMILAR TO ABOVE);  
Α VALUE 3 IF THE SPACE HAS EXACTLY TWO SPACES AROUND IT, FORMING A CORNER (THE Ζ WILL RETURN TWO TIMES, HALTING ONCE)  
Α VALUE 2 IF THE SPACE HAS TWO SPACES AROUND, FORMING A STRAIGHT LINE;  
Α VALUE 3 IF THE SPACE HAS EXACTLY ONE SPACE AROUND IT (THE Ζ HALTS FOR TWO FRAMES TO MAKE A 180 TURN).  
  
SO THE SUM OF THE VALUES OF ALL SPACES IN A LOOP-LESS PATH MUST BE AT LEAST 245.  
  
PLUS SOME SIDE CONDITIONS, LIKE:  
Α THE TOP-LEFT CORNER IS ALWAYS SPACE  
Α Κ MUST HAVE ENOUGH ROOM AT THE TOP-RIGHT TO AVOID THE Ζ.  
Α THE TOP-RIGHT CORNER MUST ALSO BE SPACE, PLUS YOU HAVE TO TAKE INTO ACCOUNT THAT IT HAS ANOTHER SPACE TO ITS RIGHT SIDE (WHICH IS OUTSIDE THE BOX BUT DOES COUNT FOR THE VALUE OF THE TOP-RIGHT SPACE INSIDE THE BOX).  
  
I FEEL THAT WITH THESE ABSTRACT RULES, IT'S NOT TOO FAR-FETCHED TO ASSUME THAT IT MIGHT BE POSSIBLE FOR HUMANS TO PROVE OR DISPROVE THE EXISTANCE OF A VALUE 245 PATH, ACTUALLY... :D

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DUSTIN                            2025-11-09 21:07
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THE MATH (SEE MY PREVIOUS COMMENT) WORKS FOR MY RUNS:  
  
| IN THE 748 RUN, THE PATH HAS TWO LOOPS:  
Α A 3X2 LOOP AT THE TOP-MIDDLE WHICH CAN EASILY BE FIXED WITH AN EXTRA Γ  
Α A 2X2 LOOP IN THE TOP-RIGHT CORNER, WHICH CAN BE FIXED BY MIRRORING THE WHOLE PATH. THIS RESULTS IN MY 758 RUN.  
  
Β HOW MANY ΑΑΑ ARE POSSIBLE EACH TIME?  
Α THE PATH IN THE 748 RUN IS ONLY GOOD FOR 116 1/2 Α (116 + ONE BONUS FRAME)  
Α BY FIXING ONLY THE 3X2 LOOP WITH THE EXTRA Γ, THIS CAN BE IMPROVED TO 118 1/2Α  
Α AND FINALLY, BY MIRRORING (758 RUN), THERE ARE 119Α POSSIBLE! (ALTHOUGH THE RUN DOESN'T SHOW IT, BUT I TESTED AT LOWER SPEED).  
  
THIS CONFIRMS (THOUGH NOT PROVES) MY THEORY THAT FOR EVERY LOOPED PATH, A BETTER NON-LOOPED PATH CAN BE FOUND!  
  
ALSO, I CALCULATED THE TOTAL VALUE OF THE LOOP-LESS PATH IN MY 758 RUN, AND THE RESULT WAS 243, TWO AWAY FROM THE 245 NEEDED FOR A PERFECT 120Α RUN. SO NOW I'M ALMOST CERTAIN THAT I DID THE METH RIGHT IN THE PREVIOUS COMMENT (FOR NON-LOOPED PATHS).  
  
I WONDER IF ONE OF nesdori'S 119Α SOLUTIONS IS IDENTICAL TO MY 758 RUN :D I GUESS IT IS, BECAUSE THAT PATH ISN'T TOO COMPLICATED ;)

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ARNO                              2025-11-20 19:33
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I'VE ALSO TRIED FOR A WHILE, BUT COULD NOT FIND A PATH FOR 120 DIAMONDS.  
  
I'M CURIOUS TO SEE THE ALTERNATIVE 119 RUNS!  
  
I DID MYSELF A RUN OF dustin'S PATH FOR 119, INCLUDING GRAPPING 119 DIAMONDS, HOWEVER, THIS CAVE SPEED MADE IT TOUGH, SO I DID IT IN THE L1 VERSION OF THIS CAVE, SEE:  
<a href="https://boulderdash.krissz.hu/cave/AatdxNZ1T0c3/dustin-s-bd25-cave-p-l1/demo/153828/" target="external">HTTPS://BOULDERDASH.KRISSZ.HU/CAVE/AATDXNZ1T0C3/DUSTIN-S-BD25-CAVE-P-L1/DEMO/153828/</a>

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DUSTIN                            2025-11-21 02:02
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NICE RUN arno! :D  
  
ALSO, THANKS FOR YOUR INTEREST IN THE LITTLE RESEARCH! IT'S REALLY A NICE MATHEMATICAL QUESTION IF EITHER A 120Α PATH EXISTS OR ITS EXISTANCE CAN BE DISPROVEN BY RELATIVELY SIMPLE MEANS :D