11 replies to this topic

[unrealdon]

Spoiler for Yep, they'd be joint leaders...

But the guy following would be 114th as he had 113 people ahead of him.  But I just used those figures for ease. Working on a similar principle, you could have 1st on 1113 points, 2nd on 1112, 3rd on 1111......113th on 1001 pts.  There would still be enough points to win comfortably.

Edit....spelling

For the sake of solution of puzzle, lets assume first person wins 131 points, second 130 and so on ... last person gets 0 points, all seperated by one point.

Edited by unrealdon, 07 August 2012 - 02:21 AM.

[bonanova]

you can take the scoring to be exactly like that in Olympics and I dont see any way one could win if he finishes 114th in all events.

bonanova is close.

Spoiler for Do even better

I guess you could juggle the points among leading contestants and push one or two more down below 1140. I had the feeling that starting out with C_i placing i^th would have the effect of top loading the best finishers thereby pushing the others down maximally, but I didn't check that option out. We have 7 points from the trailing contestants to play with, but it takes 186 points to push C₉₆ down. Someone want to find those 179 other points, have at it.

It's an interesting puzzle because there are too many contestants to just use pencil and paper, but the solution lies in a small enough corner of the search space that monte carlo methods are useless as well. Tip of the hat.