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In a bar (Posted on 2016-02-23) Difficulty: 3 of 5
N people roll a die in turn, following a prearranged list. The first to get a 6 names the drink. The second to get a 6 drinks it. The third, pays! Then the next on the list rolls and so on till the closing time.

The above goes on for 120 minutes, averaging 5 rolls per minute (the time for naming, drinking, plus settling disputes and paying the bills was discounted).

How many times was it the same player that named the drink, consumed it but did not pay for it?

a. Provide your estimates for N=3, N=6 and N=12
b. Please explain the meaning of the results.

Rem: Verification of analytical results by simulation is welcome.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Last Call Comment 6 of 6 |
(In reply to re: Last Call by Charlie)

Thanks, Charlie.  Maybe I am biased, but to me, the simulation results look close to the theoretical prediction.  All are close, and the difference is not consistently in one direction or the other.  I suppose we could do a hypothesis test, but I am not inclined.

Edited on February 25, 2016, 9:08 am
  Posted by Steve Herman on 2016-02-24 16:59:58

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