jes5199: (Default)
48: 47 46 45 44
[47 45 44 43 42 41 40 39 38 37 36 35 34 33 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 ]
( five is 24 )
LJIHGFEDCBAzyxvutsrqpnmkl1j92b3hi8c675deaf4o
126536.42 real 125734.78 user 0.00 sys

and I'm pretty much going to be awake and active from 9AM saturday, to sometime in the evening on sunday.
jes5199: (Default)
Remember when [livejournal.com profile] j3h did the peterproblem 2-36 run in 3m42.902s?
I've got it down to 1m56.343s, thanks to the geek out and the new "five rule". if anyone wants to see a really large number in base48, i may have one for you, soon.

woah: no really. i just did base40 in 4m16.806s, instead of a day and a half.
jes5199: (Default)
2. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 1_2 (1) in 0 iterations
3. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 2_3 (2) in 0 iterations
4. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 312_4 (54) in 0 iterations
5. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 413_5 (108) in 1 iterations
6. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 412_6 (152) in 6 iterations
7. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 65142_7 (16200) in 2 iterations
8. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): 7625134_8 (2042460) in 14 iterations
9. Mon Feb 20 13:37:16 PST 2006 ( 0.03s ): 8271536_9 (4416720) in 170 iterations
10. Mon Feb 20 13:37:16 PST 2006 ( 0.01s ): 9867312_10 (9867312) in 13 iterations
11. Mon Feb 20 13:37:16 PST 2006 ( 0.00s ): a98762413_11 (2334364200) in 1 iterations
12. Mon Feb 20 13:37:17 PST 2006 ( 0.07s ): b9352176_12 (421877610) in 172 iterations
13. Mon Feb 20 13:37:17 PST 2006 ( 0.05s ): cba95847213_13 (1779700673520) in 274 iterations
14. Mon Feb 20 13:37:17 PST 2006 ( 0.04s ): dcba8513492_14 (4025593863720) in 94 iterations
15. Mon Feb 20 13:37:17 PST 2006 ( 0.12s ): edcb8219473_15 (8605596007008) in 125 iterations
16. Mon Feb 20 13:37:27 PST 2006 (10.14s ): fedcb59726a1348_16 (1147797065081426760) in 52321 iterations
17. Mon Feb 20 13:37:28 PST 2006 ( 0.66s ): gfedcb93652741a_17 (2851241701975626960) in 2972 iterations
18. Mon Feb 20 13:37:28 PST 2006 ( 0.17s ): hgfedcab2514376_18 (6723295828605676320) in 536 iterations
19. Mon Feb 20 13:37:28 PST 2006 ( 0.75s ): ihgfedcb2671a3854_19 (5463472083393768444000) in 3146 iterations
20. Mon Feb 20 13:37:32 PST 2006 ( 3.09s ): jihge9137b264dc_20 (32677216797923569872) in 7387 iterations
21. Mon Feb 20 13:37:33 PST 2006 ( 1.22s ): kjihgfdbc286a4153_21 (29966837620559153371200) in 3153 iterations
22. Mon Feb 20 13:37:36 PST 2006 ( 3.16s ): lkjihgfed981c456732_22 (31992267514118823824945760) in 11241 iterations
23. Mon Feb 20 13:37:37 PST 2006 ( 1.42s ): mlkjihgfedc87521a6943_23 (39390031260941977164298669920) in 4726 iterations

and then i get stuck

update: using the Seamus inversion (a notable percentage faster) and the YARV interpreter (also, rather fast)
24. Mon Feb 20 18:14:35 PST 2006 (25.87s ): nlkjihfea679541b32dc_24 (4005106906135094120287426500) in 70603 iterations
25. Mon Feb 20 18:15:27 PST 2006 (51.51s ): onmlkjihgfdb51284e3976a_25 (141861830924325492863056534520160) in 139356 iterations
26. Mon Feb 20 18:15:35 PST 2006 ( 8.72s ): ponmlkjihgfb97461e325a8_26 (349696733550229042736767178385600) in 23162 iterations
27. Mon Feb 20 18:16:15 PST 2006 (39.38s ): qponmlkjihgfc6b72a85e3149_27 (607366984772953333470994010577018000) in 91606 iterations
28. Mon Feb 20 18:18:05 PST 2006 (110.65s): rqponmkjihf1352b69a8gd4_28 (1923262535746542596976390358681200) in 260108 iterations
29. Mon Feb 20 18:18:06 PST 2006 ( 1.09s ): srqponmlkjihgfdc2619485ba37_29 (3049240241702704989143250469319645548800) in 2657 iterations


update: at home, not as nice of a setup, but left alone for a couple hours
30. Mon Feb 20 19:54:21 GMT-8:00 2006 (621.61s ): tsrqonmlji2b1e4h8g397d6_30 (9403123287053212444852754413479696) in 608567 iterations
31. Mon Feb 20 19:54:41 GMT-8:00 2006 (19.70s ): utsrqponmlkjihge89a265d41bc37_31 (17742152322257126982068381069905735557988800) in 36417 iterations
32. Mon Feb 20 20:44:17 GMT-8:00 2006 (2975.51s ): vutsrqponmlkjihf1758a9bc324e6dg_32 (45624400749143691515203426155119190014607956400) in 5223796 iterations
33. Mon Feb 20 20:44:28 GMT-8:00 2006 (11.72s ): wvutsrqponlkjihg7c813d59ae426_33 (108762688293940170615524635720390804084605600) in 19124 iterations
34. Mon Feb 20 20:55:00 GMT-8:00 2006 (631.11s ): xwvutsrqponmlkjieb72963c458f1da_34 (298845997702564900630439027811497500681804706400) in 1080462 iterations
35. Mon Feb 20 20:59:26 GMT-8:00 2006 (266.50s ): yxwvutrqponmkjibcg16h59328d4a_35 (599235365197015473511633715765960442230707200) in 190231 iterations
36. Mon Feb 20 21:13:10 GMT-8:00 2006 (824.16s ): zyxwvutsqponmlkjf586a4e2b13d7hc_36 (1758016119625362949735212719023837052237619732000) in 1382374 iterations
jes5199: (Default)
so, when my head starts to hurt from working on computer things that aren't fun, i've gotten in the habit of switching over to doing things with the computers that are fun, rather than just filling with hate and bile for the machines. So I've been working on calculating [livejournal.com profile] pmb's number series (A113028). It's the sort of problem where you can get a few answers without much work, but the difficulty of each number in the sequence escalates pretty fast.

So I unexpectedly solved base 16 yesterday, and I called Peter immediately. Peter has encouraged me to talk about my latest method- the one that produced Base 16's answer (0xfedcb59726a1348). Well, I think it's base 16's answer- it's hard to prove! (Base 17 just gave me one that was visibly wrong. Hrm. One of my computers is lying.)

Anyway, there's three rules that all are in play to find the right number.
  1. Answers must be as big as possible
  2. Answers must not repeat digits or contain zeros
  3. Answers must be divisible by all of their digits

Well, these distill down to:
  1. Start at the top, nn-1 is the approximation of that I use, but rules 2 and 3 make it a bit lower in reality
  2. Answers must be contained in the series of lexicographic permutations of digits (321, 312, 231, 213, 132...)
  3. Answers must be a multiple of the Least Common Multiple of the digits they are made of

So, most of the time, the best way to find an answer is to start at the multiple of the LCM nearest nn-1, and just subtract the LCM over and over and test to whether it has repeated digits or zeros. But once we reach base 6, there are these huge regions of numbers where the lexicographic permutations are much further apart than the multiples of the LCM are. For example, in base 8, 67123458 and 65743218 are adjacent lexicographically, but there are 46 multiples of the LCM between them. As the bases get higher, the gains you get by skipping such ranges get larger, quickly.
jes5199: (Default)
irb(main):002:0> "fedcb59726a1348".to_i(16).pmbgood(16)
=> true
irb(main):003:0> "fedcb59726a1348".length
=> 15
irb(main):004:0> "fedcb59726a1348".to_i(16).pmbbad(16)
=> nil
irb(main):005:0> "fedcb59726a1348".to_i(16)
=> 1147797065081426760

March 2016

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