20210802, 11:42  #1 
Jul 2015
2^{2}·7 Posts 
August 2021

20210802, 12:30  #2  
Feb 2017
Nowhere
1409_{16} Posts 
This reminds me of a problem in The 2nd Scientific American Book of Mathematical Puzzles & Diversions, a collection of Martin Garner's "Mathematical Games" columns from Scientific American, of which a PDF may be found here. It is the ninth of the first set of "Nine Problems."
Different versions may be found online, generally without any attribution or reference to earlier versions. Here is Gardner's version: Quote:
Quote:


20210906, 07:17  #3 
Oct 2017
171_{8} Posts 
The publication of the solution wasn’t helpful for me.
Can anyone explain the strategy: “All players are perfectly rational  they always choose which player to remove in a way that maximizes their chance to win.” ? I wasn’t able to solve the challenge, because I couldn’t reproduce the values of the second example. The strategy of the first example was: “Always remove the best”. The values of the challenge were the exact values and could be computed with pencil and paper. Using this strategy for the second example (5 players) yielded approximately: 0,24416 0,18885 0,18867 0,17317 0,20514 So the simple strategy (removing the best) is wrong. 
20210906, 11:24  #4 
Jan 2017
2^{3}·3·5 Posts 
Yes, that is not always the correct strategy for the participants. If you haven't seen the triangular duel puzzle before, see that for analysis ("deliberately miss" may not be a directly valid option here, but can be simulated by adding dummy participants).

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