All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
Chess Strategy (Posted on 2006-08-01) Difficulty: 2 of 5
A man has to win two games in a row in order to win a prize. In total, he has to play only three games. The opponents are weak or strong. He has to at least play one strong opponent, and he cannot play consecutively two weak opponents. What sequence should he choose to play?

No Solution Yet Submitted by Salil    
Rating: 3.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: probablistic proof :-D | Comment 5 of 7 |
(In reply to probablistic proof :-D by Daniel)

the odds of getting two in a row are


Actually the prob is s*(1-(1-w)*(1-s)) = s*(w+s-w*s)

The formula given by Daniel counts the event of wins against all three twice, once as wins against the first two and once as wins against the last two.

odds of getting two in a row here are

Actually w*(1 - (1-s)^2) = 2*s*w - w * s^2

not mentioned by Daniel is wsw, where the prob is

s*(1 - (1-w)^2) = 2*w*s - s * w^2

2*s*w - w * s^2,
from w>s it follows that

sw > s^2
2sw-ws^2 > sw - ws^2 + s^2
2sw-ws^2 > s(w+s-ws)

so sws beats wss or ssw.

2*s*w - w * s^2
2*w*s - s * w^2

the former is larger as a smaller amount is being subtracted from the same first term.

So sws is best.

  Posted by Charlie on 2006-08-01 11:40:04
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information