Problem 481

Anton_Lunyov · Post by **Anton_Lunyov** » Sun Sep 21, 2014 4:08 am

It is not accessible and side says:
Problem 481 will be accessible in 23 hours, 52 minutes (Sat, 20 Sep 2014, 20:00)
Current date/time on server: Sat, 20 Sep 2014, 20:08
The same was for 480 but it gets accessible in 3-4 minutes.

euler · Post by **euler** » Sun Sep 21, 2014 10:57 am

Thank you for reporting it. I think that I located the bug and it should now be fixed.

Garrit · Post by **Garrit** » Sun Sep 21, 2014 10:34 pm

Two questions:
1.
It seems there is a infinite recursion, it is possible that each chef get an unfavorable rating ever single turn forever, and this will obviously tend to zero as the turns tend to infinity, but, the computer doesn't necessarily know that. What am I missing about this question? if they get an unfavorable rating are they eliminated automatically?

2.
What happens with the chef probabilities on each round where an elimination occurs?
Say chef one gets a favorable rating, and eliminates chef 14.
does chef 2 have S(2)=[frac]F₂,F₁₅[/frac] or S(2)=[frac]F₂,F₁₄[/frac] ?

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Marcus_Andrews · Post by **Marcus_Andrews** » Sun Sep 21, 2014 11:04 pm

Garrit:

1. As you say, it is possible for that to happen. Can you take this into account somehow?

2. In this competition, you are not directly eliminated for having an unfavorably-rated dish. You are eliminated if another chef gets a favorable rating who then chooses to eliminate you.

3. A chef's skill level is assigned at the start of the tournament, and it does not change at any time.

noms · Post by **noms** » Tue Dec 09, 2014 10:01 am

(results removed by moderator)

noms · Post by **noms** » Sat Dec 13, 2014 2:16 pm

Nobody ?

Marcus_Andrews · Post by **Marcus_Andrews** » Sat Dec 13, 2014 5:25 pm

As per the big red box near the top of this page, please do not discuss partial results/spoilers or ask for hints.

viewtopic.php?f=50&t=1356#p12839
viewtopic.php?f=50&t=1989#p21039

That being said: In general, if you can't get the math to work out for a particular case, it usually helps to tackle a simpler case first. There are actually clarification posts in this very thread that should help as well.

noms · Post by **noms** » Sun Dec 14, 2014 12:55 pm

Thank you Markus for your answer and sorry

for my "spoil". With more than hundred answer to this problem, I was thinking that my three lines of "code" was not a problem (sorry for my poor English). I don't need Math for this problem but only need to know if I am right in thinking that, with three chefs, #1, #2, #3, the next player after chef #3 is chef#1... Or my compréhension of English is too bad.

Marcus_Andrews · Post by **Marcus_Andrews** » Sun Dec 14, 2014 3:47 pm

Yes, it'd be chef #1's turn again (assuming he/she is not eliminated by chef #3).

noms · Post by **noms** » Sun Dec 14, 2014 5:33 pm

And then, in the case S(1) = 0.25, S(2) = 0.5 and S(3) = 1, am I right or not when I find W3(1) = 0.2 and not W3(1) = 0.29375 ?

Marcus_Andrews · Post by **Marcus_Andrews** » Sun Dec 14, 2014 6:07 pm

W₃(1) = 0.29375 is the correct result.

damiengif · Post by **damiengif** » Fri Mar 09, 2018 2:24 pm

This problems reminds me of the 'El Jj truel' problem
http://eljjdx.canalblog.com/archives/20 ... 18907.html

Likewise, on his first turn, chef #1 should rather make sure that his dish won't be assessed favorably.
His probability of winning will become greater : W3(1) = 0.325

This violates problem 481 rule : "On each chef's turn, he/she cooks up a dish to the best of his/her ability".
But, we could consider "cheating" as a strategy

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