February 2020
 

[url]http://www.research.ibm.com/haifa/ponderthis/challenges/February2020.html[/url]

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 *.

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

[QUOTE=KangJ;536858]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[/QUOTE]

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.

[QUOTE=Dieter;536863]Very impressive.

But it is a search of the needle in the haystack (is that a germanism?).
[/QUOTE]

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?:smile:

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

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?

[QUOTE=yae9911;537384]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?[/QUOTE]

I am finding 33.33333333333334

Thanks! :thumbs-up:

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...[/code]

[QUOTE=yae9911;537390]Thanks! :thumbs-up:

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...[/code][/QUOTE]

Wow!

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?

There are ~100[SUP]20[/SUP] 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!