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Old 2020-01-29, 17:07   #1
what
 
Dec 2019
Kansas

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Default February 2020

http://www.research.ibm.com/haifa/po...ruary2020.html
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Old 2020-02-05, 09:19   #2
Dieter
 
Oct 2017

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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
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Old 2020-02-06, 07:16   #3
KangJ
 
Jul 2015

910 Posts
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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
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Old 2020-02-06, 09:27   #4
Dieter
 
Oct 2017

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Quote:
Originally Posted by KangJ View Post
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.
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Old 2020-02-07, 09:56   #5
Kebbaj
 
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"Kebbaj Reda"
May 2018
Casablanca, Morocco

5510 Posts
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Quote:
Originally Posted by Dieter View Post
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
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Old 2020-02-11, 20:55   #6
yae9911
 
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"Hugo"
Jul 2019
Germany

31 Posts
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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?
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Old 2020-02-11, 21:29   #7
SmartMersenne
 
Sep 2017

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Quote:
Originally Posted by yae9911 View Post
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
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Old 2020-02-11, 21:50   #8
yae9911
 
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"Hugo"
Jul 2019
Germany

31 Posts
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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...
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Old 2020-02-11, 21:51   #9
SmartMersenne
 
Sep 2017

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Quote:
Originally Posted by yae9911 View Post
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!
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Old 2020-02-12, 19:04   #10
Dieter
 
Oct 2017

89 Posts
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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?
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Old 2020-02-12, 22:17   #11
SmartMersenne
 
Sep 2017

1158 Posts
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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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