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 Showing results 1 to 25 of 36 Search took 0.01 seconds. Search: Posts Made By: 0scar
 2021-07-06, 11:45 Replies: 9 Views: 1,774 Posted By 0scar Great explanation from the given subforum. ... Great explanation from the given subforum. About efficiently computing square roots modulo a large prime (hundreds of digits or more), there are two good algorithms by Tonelli-Shanks and by Cipolla.
 Forum: Puzzles 2021-07-01, 03:25 Replies: 35 Views: 6,099 Posted By 0scar Actually, it seems that I spoiled it before.... Actually, it seems that I spoiled it before. Within this thread, I was the first one to say "Leyland" (should I say "xilman"?) Wikipedia page about Leyland numbers mentions the largest known...
 Forum: Puzzles 2021-06-26, 04:41 Replies: 35 Views: 6,099 Posted By 0scar Your findings below 10^1000 also match mine. 25... Your findings below 10^1000 also match mine. 25 solutions up to 10^1000. 34 solutions up to 10^2000. 46 solutions up to 10^3000. Or less? Last 12 candidates only passed a BPSW test, I stopped...
 Forum: Puzzles 2021-06-22, 20:10 Replies: 35 Views: 6,099 Posted By 0scar My bottleneck is primality proving. I used YAFU... My bottleneck is primality proving. I used YAFU implementation of APR-CL for solutions with less than 2k digits.
 2021-06-13, 08:51 Replies: 10 Views: 3,020 Posted By 0scar With your "trigonometric" approach, you use... With your "trigonometric" approach, you use integer parameters a and b to build a Pythagorean triplet A,B,C: A = 2*a*b, B = b^2 - a^2, C = a^2 + b^2. Then you generate a candidate solution: x =...
 Forum: Puzzles 2021-03-20, 20:20 Replies: 27 Views: 5,462 Posted By 0scar After such an explicit challenge... 96... After such an explicit challenge... 96 words: 000100010001000 000100010001000 000100010001000 110001000100011 000010001000000 000000100010000 000100010001000
 Forum: Puzzles 2021-02-13, 04:25 Replies: 27 Views: 5,462 Posted By 0scar Block-version is the most interesting one. I... Block-version is the most interesting one. I slightly modifìed my candidate to fit your additional constraint. Less words, but more symmetries. 86 words: 000100010001000 000100010001000...
 Forum: Puzzles 2021-02-08, 04:24 Replies: 27 Views: 5,462 Posted By 0scar nice puzzle; not sure about minimality of my... nice puzzle; not sure about minimality of my candidates. "bars" version, fixing 150-word near-solution by Dr Sardonicus. 5 words and 4 bars per row/column; 150 words, 120 bars placed along 8...
 Forum: Puzzles 2020-12-06, 19:08 Replies: 3 Views: 2,933 Posted By 0scar The published four-step base solution is flawed. ... The published four-step base solution is flawed. At the very first step, (2^2)^31 is equal to 2^(2*31), not to 2^(2^31). We can get a working four-step solution by modifying the starting list to...
 Forum: Puzzles 2020-11-08, 07:57 Replies: 34 Views: 9,351 Posted By 0scar For bonus problem, there's some trade-off between... For bonus problem, there's some trade-off between code length and code speed. The published solution uses 12 lines and needs 16 steps to reach 1970 paths. I worked on minimizing the number of steps...
 Forum: Puzzles 2020-11-08, 02:48 Replies: 34 Views: 9,351 Posted By 0scar As an example, we can try to minimize code... As an example, we can try to minimize code length. In this sense, published solutions are hard to beat. For base problem, we can save one line by applying the CHAOS trick described in post #23....
 Forum: Puzzles 2020-11-06, 03:12 Replies: 34 Views: 9,351 Posted By 0scar I still believe that variable "Z" stands for... I still believe that variable "Z" stands for "Zaphod Beeblebrox" :-)
 Forum: Puzzles 2020-11-05, 08:32 Replies: 34 Views: 9,351 Posted By 0scar As a joke, we could say that few people were... As a joke, we could say that few people were stupid enough to solve the puzzle
 Forum: Puzzles 2020-11-04, 17:30 Replies: 34 Views: 9,351 Posted By 0scar I don't fully understand the second block of code... I don't fully understand the second block of code within published base solution. I suppose that new code lines must be inserted as follows: If a and b are non-negative integers with a >= b,...
 Forum: Puzzles 2020-10-23, 09:41 Replies: 34 Views: 9,351 Posted By 0scar The "trick" itself is just one more degree of... The "trick" itself is just one more degree of freedom in writing code. Of course I can remove all "tricky" edges from my solutions; the easiest way requires to keep the same number of...
 Forum: Puzzles 2020-10-21, 11:10 Replies: 34 Views: 9,351 Posted By 0scar I agree at 100% with you. Had it been... I agree at 100% with you. Had it been necessary, writing it would have been too spoiling. I only wrote that I found it useful (shorter code, faster reaching 1970)
 Forum: Puzzles 2020-10-21, 02:39 Replies: 34 Views: 9,351 Posted By 0scar I wish I could call you "pessimistic". Looking... I wish I could call you "pessimistic". Looking at the past three years, Oct20 seems somehow similar to Nov17, another "find-constrained-algorithm" challenge. Nov17 was actually solved by 23 people...
 Forum: Puzzles 2020-10-14, 09:04 Replies: 34 Views: 9,351 Posted By 0scar In my opinion, May19 and Oct18 (different area... In my opinion, May19 and Oct18 (different area triangles) were much harder than Oct20. Perhaps now many frequent solvers actually submitted wrong solutions or no solutions at all due to the...
 Forum: Puzzles 2020-10-12, 18:09 Replies: 34 Views: 9,351 Posted By 0scar "I think I'm paranoid / And complicated..." ... "I think I'm paranoid / And complicated..." (Garbage, Version 2.0, 1998) At least, now the text seems unambiguous enough to ponder this problem...
 Forum: Puzzles 2020-10-12, 03:06 Replies: 33 Views: 14,073 Posted By 0scar I followed uau's suggestion. Given a RPS(n)... I followed uau's suggestion. Given a RPS(n) game, we can always extend it to a RPS(n+2) game: aaavw aaavw aaa10 ww001 vv100 where A is the adjacency matrix of the RPS(n) game, V is a column...
 Forum: Puzzles 2020-10-11, 10:31 Replies: 33 Views: 14,073 Posted By 0scar After a slight modification, uau's "algebric"... After a slight modification, uau's "algebric" construction also explains the RPS(13) game with 39 automorphisms (which is optimal, according to the paper referenced within September's solution)....
 Forum: Puzzles 2020-10-07, 05:28 Replies: 33 Views: 14,073 Posted By 0scar A very elegant construction, thanks uau! ... A very elegant construction, thanks uau! Another nice construction works for composite n and solves n=9. Given two games RPS(a) and RPS(b), build a game RPS(a*b). Let z = x*b+y, with...
 Forum: Puzzles 2020-10-06, 10:53 Replies: 33 Views: 14,073 Posted By 0scar As a lucky guess, I searched for RPS(n) games... As a lucky guess, I searched for RPS(n) games which admit at least one n-cycle as an automorphism. So they admit at least n automorphisms (by repeatedly applying the cyclic shift). Can we get n*q...
 Forum: Puzzles 2020-10-06, 10:41 Replies: 34 Views: 9,351 Posted By 0scar Unless it implies that the chaos operator can let... Unless it implies that the chaos operator can let the program move to next instruction or force a jump to an instruction from the list, an even more "chaotic" (and undocumented) behaviour.
 Forum: Puzzles 2020-09-12, 03:25 Replies: 33 Views: 14,073 Posted By 0scar I didn't know the chosen "cycle notation" too, I... I didn't know the chosen "cycle notation" too, I always used the "one-line notation" described by SmartMersenne. Wikipedia has an useful paragraph about them...
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