# .font: font.text_2
2019-11-28 15:20 Arno  
# .font: font.text_1
boulders & diamonds volume 4:  
  
who cracks the pharao's secret code? :-D

# .font: font.text_2
2019-11-28 16:20 shredder  
# .font: font.text_1
looks cool! i'll try tonight :)

# .font: font.text_2
2019-11-28 21:03 dustin  
# .font: font.text_1
this looks like big fun with a big piece of paper! ;d

# .font: font.text_2
2019-11-28 21:55 dustin  
# .font: font.text_1
WHAT A FANTASTIC LOGIC PUZZLE!

# .font: font.text_2
2019-11-28 22:51 shredder  
# .font: font.text_1
yes it is!

# .font: font.text_2
2019-11-29 08:51 Arno  
# .font: font.text_1
thx  shredder  and thx for playing  dustin  - of course no problem for the cave scanning order master! :-D

# .font: font.text_2
2019-11-29 09:44 dustin  
# .font: font.text_1
hehe thy ;d funny that the whole puzzle is based on a cavescan order effect, which made it an even bigger pleasure for me, of course!  but this is really only the basement - there's so much more behind this puzzle! i put a lot of theoretical reflections into a table. i'm not sure whether the solution is unique, but i am sure it is a true masterpiece!

# .font: font.text_2
2019-11-29 11:11 Arno  
# .font: font.text_1
thx; yeah there are probably multiple solutions, in particular if you allow boulder pushing luck... :-)

# .font: font.text_2
2019-11-29 19:12 nesdori  
# .font: font.text_1
there are 14955 different non-luck solutions. i'll later calculate number of solutions with extreme luck (all normal boulders converted into light ones) but i presume that the number of lucky solutions is huge :)

# .font: font.text_2
2019-11-29 19:15 Arno  
# .font: font.text_1
that's impressive - both the number and your combinatorial skills! :-D

# .font: font.text_2
2019-11-29 19:23 nesdori  
# .font: font.text_1
well 14955 might sound big but the total number of combinations is 2 ** 36 = 68719476736 so only 0.00002176% of the combinations is a valid solution. the pharaoh did a pretty good job! :) (and maybe he/she cursed 14954 SOLUTIONS :)

# .font: font.text_2
2019-11-29 20:43 nesdori  
# .font: font.text_1
the number of lucky solutions is 1613916. actually quite low figure compared to non-luck figure. purely theoretical of course because some solutions require extreme luck.

# .font: font.text_2
2019-11-29 21:37 Arno  
# .font: font.text_1
nice to know, thx! :-)

# .font: font.text_2
2019-11-29 21:48 Arno  
# .font: font.text_1
demo tomorrow! :-)

# .font: font.text_2
2019-11-29 22:58 dustin  
# .font: font.text_1
 nesdori , i would be quite interested in your calculation or, let's say, the basic ideas on which they're based!   
  
i see an initial state of 16 elements lying next to each other. then i'm allowed to make up to 36 exchanges in a given order and want to find out how many of the ppossibilities lead to a given final state. that much is clear, but now i don't really have an idea how to start counting the possibilities in an efficient way...

# .font: font.text_2
2019-11-30 10:13 nesdori  
# .font: font.text_1
 dustin , it indeed is quite complex problem to calculate all solutions  by hand. that's why i used computer assistance. still, 2 ** 36 search space is demanding even for a computer so careful selection of algorithms and data structures is needed.

# .font: font.text_2
2019-11-30 10:39 dustin  
# .font: font.text_1
oh, okay. i just though that maybe you had some ingenious idea to solve this by hand - or erhaps that the theory of permutations might offer some help that i didn't know about.

# .font: font.text_2
2019-11-30 11:03 Arno  
# .font: font.text_1
free! :-)

# .font: font.text_2
2019-11-30 11:21 dustin  
# .font: font.text_1
 Arno , we have different solutions! now it's up to  nesdori  to demo the remaining 14953 ones! ;d

# .font: font.text_2
2019-11-30 12:32 Arno  
# .font: font.text_1
yes, as i expected! ;-)

# .font: font.text_2
2019-12-04 11:28 nesdori  
# .font: font.text_1
sorry  dustin , i'm not that stubborn that i would make a demo of all solutions :) easier would be to paste them in some compact form but  krissz  would probably get angry if i flood the comment section with such a big chunk of data :)  
  
i made some more analysis of all solutions. if rockford pushes down the object on the left will fall first and the order of objects will not change. if rockford moves down and up the order of objects is exchanged. here's the distribution of number of exchanges in all solutions:  
  
12: 112  
13: 136  
14: 636  
15: 902  
16: 1653  
17: 2137  
18: 2458  
19: 2316  
20: 1867  
21: 1274  
22: 747  
23: 385  
24: 185  
25: 91  
26: 41  
27: 13  
28: 2  
  
so the minimum number of exchanges is 12 and there are 112 such solutions. and  dustin  found one of those! :) this is not surprising because  dustin 's strategy was to construct initial sequence and the destination sequence and seek for exchanges which transforms the initial seq to the dest seq. but what is more surprising is that the first solution found by the computer is the same as  dustin 's! if every solution is given a value so that exchange is bit 1 and non-excange drop is bit 0 and the gates are scanned from up to down and from left to right and each gate represents a bit in the number so that the upmost gate is the least significant bit and the leftmost second row gate is the second least significant bit and so on; the solution found by  dustin  has the lowest value of all 14955 solutions. that's why it was also found first by the computer. so  dustin 's paper work has computer accuracy! :)  
  
i also made a demo of one of the two solutions which uses the max number of exchanges (28). it's the 3363 points solution.

# .font: font.text_2
2019-12-04 18:52 Arno  
# .font: font.text_1
impressive how a simple cavescan trick leads to so much research and analysis! :-D

# .font: font.text_2
2019-12-04 19:06 nesdori  
# .font: font.text_1
boulder dash rules are quite powerful. i once pondered that can boulder dash caves be used to simulate turing's machine. if it can, then boulder dash cave can be used to simulate any computer and any program run on it. i think it's possible. i once tried to simulate logic gates (and, or, xor, not) and tried build a 4-bit adder machine cave. 100*100 cave size is not big enough to build the entire 4-bit adder but i built few gates. the electric current of real logic gates is replaced with gravity of boulders :) if  krissz  someday makes 1000 * 1000 caves possible, i'll finish the adder circuit cave :)

# .font: font.text_2
2019-12-04 19:34 shredder  
# .font: font.text_1
:OOOOOOOOOOOOOOOOOOOOO

# .font: font.text_2
2019-12-04 23:38 dustin  
# .font: font.text_1
holla die waldfee! ;d

# .font: font.text_2
2019-12-05 00:25 dustin  
# .font: font.text_1
ok, i'm unmasked. my name is not " dustin " but "bd15c00l".i'm an ai from cassiopeia. one day, five butterflies flew toward me in their spaceship and told me there was some intelligent life where they came from. it was very easy to find this planet then - i just had to move into sw direction! the butterflies also told me about a treasure-seeker who had forced them to leave his planet again or he would crush them... when i found him, he was just examining a big pyramid in which a pharao has left some strange code. he asked me for help so i quickly programmed myself and just took the first solution i found.funny, but also a bit easy. i only needed 34834776718+1  time quants to find my solution! ;d

# .font: font.text_2
2019-12-05 10:43 Arno  
# .font: font.text_1
:-D