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 2020-01-29, 17:07 #1 what   Dec 2019 Kansas 100002 Posts February 2020
 2020-02-05, 09:19 #2 Dieter   Oct 2017 11001012 Posts Some remarks for comparison, testing,... The exact value of the expected number of moves of the given example (Milton Bradley game) containing 9 ladders and 10 snakes is: Numerator: 225837582538403273407117496273279920181931269186581786048583 Denominator: 5757472998140039232950575874628786131130999406013041613400 computed by Althoen, King, Schilling without using floats (!!!) in 1993. That is = 39,225122308234960369445... My code using simple double precision flaoting point values (64 Bit) yields 39,225122308234909. So 64 bit should be sufficient for the challenge - perhaps not for the „*“. For the challenge itself I use brute force. Two days ago I have submitted a combination of pairs yielding 66,97870454786... Meanwhile I have found 66,9787048756..., but I am far away from *. Last fiddled with by Dieter on 2020-02-05 at 09:21
 2020-02-06, 07:16 #3 KangJ   Jul 2015 10012 Posts So far, I got 15 different solutions. The speed of my code is approximately 1 solution / 3~4 hours. (I used brute-force method with a little bit of optimization.) Can I eventually get the bonus '*' in February? I don't know. Below is the obtained solutions and the errors until now. Solutions (Expected moves) Errors 66.978705461630 0.000000454075 66.978704620197 0.000000387358 66.978705335723 0.000000328168 66.978704680018 0.000000327537 66.978704698700 0.000000308855 66.978704705772 0.000000301783 66.978705293440 0.000000285885 66.978705290182 0.000000282627 66.978705240145 0.000000232590 66.978704841683 0.000000165872 66.978705149669 0.000000142114 66.978704904408 0.000000103147 66.978705103018 0.000000095463 66.978705033187 0.000000025632 66.978705009608 0.000000002053
2020-02-06, 09:27   #4
Dieter

Oct 2017

101 Posts

Quote:
 Originally Posted by KangJ So far, I got 15 different solutions. The speed of my code is approximately 1 solution / 3~4 hours. (I used brute-force method with a little bit of optimization.) Can I eventually get the bonus '*' in February? I don't know. Below is the obtained solutions and the errors until now. Solutions (Expected moves) Errors 66.978705461630 0.000000454075 66.978704620197 0.000000387358 66.978705335723 0.000000328168 66.978704680018 0.000000327537 66.978704698700 0.000000308855 66.978704705772 0.000000301783 66.978705293440 0.000000285885 66.978705290182 0.000000282627 66.978705240145 0.000000232590 66.978704841683 0.000000165872 66.978705149669 0.000000142114 66.978704904408 0.000000103147 66.978705103018 0.000000095463 66.978705033187 0.000000025632 66.978705009608 0.000000002053
Very impressive.
Meanwhile my best is 66,9787050875 (error = 8*10^(–8).
But it is a search of the needle in the haystack (is that a germanism?).
If I have a good value and if I change one parameter in one [source,target] pair, I get a totally different bad value. So I let work 8 threads and I am happy that we have a leap year.

2020-02-07, 09:56   #5
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

2·31 Posts

Quote:
 Originally Posted by Dieter Very impressive. But it is a search of the needle in the haystack (is that a germanism?).
Nadel im Heuhaufen suchen. The expression Dieter is not only Germanic. Also a lot to use in French: " Chercher une aiguille dans une botte de foin". Also in many languages. "look for a needle in a haystack". "Buscar una aguja en pajar"...
Oddly it does not exist in my native language ?, "Rachid naimi" Can you confirm that !. If it has an equivalent?

For those who didn't know the game like me, here is a link. Its helped me better understand the question:
https://www.crazygames.com/game/snakes-and-ladders

 2020-02-11, 20:55 #6 yae9911     "Hugo" Jul 2019 Germany 31 Posts May I ask you for a little help? The article by Althoen, King and Schilling states: The expected playing time for a 100-square game played with a six-sided die (...neither snakes nor ladders), i.e., the empty board. It is almost exactly 33 moves. I cannot reproduce this value, but get slightly more: 33.3... What expected game time do you get for the empty board?
2020-02-11, 21:29   #7
SmartMersenne

Sep 2017

22·23 Posts

Quote:
 Originally Posted by yae9911 May I ask you for a little help? The article by Althoen, King and Schilling states: The expected playing time for a 100-square game played with a six-sided die (...neither snakes nor ladders), i.e., the empty board. It is almost exactly 33 moves. I cannot reproduce this value, but get slightly more: 33.3... What expected game time do you get for the empty board?
I am finding 33.33333333333334

 2020-02-11, 21:50 #8 yae9911     "Hugo" Jul 2019 Germany 31 Posts Thanks! Well then I don't have to worry about it anymore. I got both with the random simulation, with which I can recalculate the original game quite accurately, and with an exact calculation the approx. 33.333 ... The exact result should be Code: 77793808048991155069512637767746406705805011749411165293240199952210986407 / 2333814241469732031952625840042216151324387397379954245052697639351484416 = 33.33333333333337075608827723...
2020-02-11, 21:51   #9
SmartMersenne

Sep 2017

22·23 Posts

Quote:
 Originally Posted by yae9911 Thanks! Well then I don't have to worry about it anymore. I got both with the random simulation, with which I can recalculate the original game quite accurately, and with an exact calculation the approx. 33.333 ... The exact result should be Code: 77793808048991155069512637767746406705805011749411165293240199952210986407 / 2333814241469732031952625840042216151324387397379954245052697639351484416 = 33.33333333333337075608827723...
Wow!

 2020-02-12, 19:04 #10 Dieter   Oct 2017 6516 Posts The solvers list has been updated. There is only one solver with „*“. Meanwhile my best combination has an error of 1,555*10**(-9). Has anyone of you significantly better values?
 2020-02-12, 22:17 #11 SmartMersenne   Sep 2017 10111002 Posts There are ~10020 possible combinations. It is like the puzzle-master is saying "I have a combination in mind, can you find it?" There doesn't seem to be any clue as to how to find it. And we all have been trying for the last 2 weeks to find it by random search. Good luck!

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