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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(7): regarding posted solution | Comment 45 of 46 |
(In reply to re(6): regarding posted solution by Ravi Raja)

It is not required that the maximum and minimum numbers be known in order for the posted strategy to need a modification. What I stated previously in clarifying Cory's point was an example of 100 slips. The only thing we know about the maximum is that it is at least 100; it might be 10,000,000 for all we know. The only thing we know about the minimum is what we see come up. But it still holds true that if every one of the first 37 was under 50, it still makes no sense to accept an 80. This is even though we do not know the distribution and do not know the maximum, all we know is that because each slip has a unique number, that the maximum, whatever it is, is at least 100 and maybe more (maybe a lot more). But we dont know what it is, just that it's at least 100.

As Cory said it's the uniqueness of the slips, and not the knowing of the min and max, that changes the nature of the strategy.
  Posted by Charlie on 2003-03-29 09:59:35

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