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 2022-06-02, 00:28 #1 Xyzzy     Aug 2002 100001000110102 Posts June 2022
 2022-06-15, 13:36 #2 dg211   Jun 2016 238 Posts To help people check their answers without spoiling the puzzle, these were the last two digits of each of my values for n up to 20. 00, 01, 03, 11, 35, 08, 80, 48, 14, 23, 34, 49, 46, 37, 33, 34, 76, 71, 38, 52
 2022-06-17, 23:51 #3 uau   Jan 2017 2·73 Posts Has anyone here tried to calculate values especially far? I've computed up to 23 (with a fast enough program that calculating the next few values would be realistic if I left it running for a while).
2022-06-19, 05:30   #4
Dieter

Oct 2017

12610 Posts

Quote:
 Originally Posted by dg211 To help people check their answers without spoiling the puzzle, these were the last two digits of each of my values for n up to 20. 00, 01, 03, 11, 35, 08, 80, 48, 14, 23, 34, 49, 46, 37, 33, 34, 76, 71, 38, 52
n=21: …77 ?

2022-06-19, 09:58   #5
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

32·11 Posts

Quote:
 Originally Posted by uau Has anyone here tried to calculate values especially far? I've computed up to 23 (with a fast enough program that calculating the next few values would be realistic if I left it running for a while).
@uau
For confirmation :
n 22 finish by 39
n 23 finish by 62

 2022-06-19, 14:03 #6 uau   Jan 2017 2228 Posts Those values match what I got. There are some things I'd say about the calculation, but they'd be kind of spoilery, so perhaps better left for private messages or after the month is over.
 2022-06-20, 09:47 #7 dg211   Jun 2016 100112 Posts My (fairly naive, single-threaded) code took about two and a half hours to do n=20, and it goes up by a factor of about 4 for each increase in n. By multithreading it I think I could do n=23 or even n=25 in a not totally absurd time, but wondering if other people have faster approaches?
 2022-06-20, 13:42 #8 uau   Jan 2017 14610 Posts Well my code is faster, but not a totally different approach - still proportional to the overall number of polyominoes. I'll send details in PM.
 2022-06-21, 17:29 #9 KangJ   Jul 2015 10112 Posts Question about algorithm I am seriously struggling with this problem. If there is an algorithm that efficiently creates polyomino without duplicates, what would it be? The method of creating and saving all polyominos to check for duplicates is easily limited around N=15. Is it correct to save all polyominos of size N-1 to create a new polyomino of size N? I tried to classify polyominos by width size, but the method of saving all polyominos to check for duplicates also runs into a limit as N increases.

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