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The Best Strategy (Posted on 2003-03-18) Difficulty: 5 of 5
A box is filled with 'N' slips of paper. On each slip of paper is written some positive integer (note that any positive integer may appear on the slips - not just the integers from 1 to 'N'). The integers do not necessarily appear in any sequence or pattern. Each of the slips has a different integer on it, so there is just one slip with the greatest integer.

A person who has no prior knowledge of which numbers appear on the slips - but who does know that there are 'N' slips - is to blindly pull slips from the box one by one. The person looks at each slip, then either agrees to accept that number (of Rupees) and quit or decides to go on and choose another slip.

Note that the person looks at each slip as he/she proceeds, and then decides whether to quit or to go on. That person can go forward, but cannot go back. If no choice is made by the time the 'N'th slip is reached, then the person must accept the number (of Rupees) on the 'N'th slip.

Does there " EXIST " a 'Best Strategy' for the person ? If " YES ", then what is that strategy ? (Here the term " Best Strategy" means that the person will get the greatest amount of Rupees).

See The Solution Submitted by Ravi Raja    
Rating: 4.1818 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): What's the distribution? | Comment 18 of 46 |
(In reply to re: What's the distribution? by Ravi Raja)

So, apparently this is indeed intended to be the classic problem, that is, to maximize the probability of getting the sole highest slip of paper, rather than maximize the expected value of the winnings, that I had assumed it to be.
  Posted by Charlie on 2003-03-19 03:41:14

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