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).
(In reply to
re(5): regarding posted solution by Cory Taylor)
There it is Cory I have found out the comment that I have mentioned in my previous comment and that was posted by pleasance with the subject: "re(3): the solution", in which he comments the following:
"In the case unlimited integers, I think your strategy only works if you have no clue whatsoever what the highest number is likely to be, not even the order of magnitude, and that you choose one slip or more among the ones to be discarded that is >> n".
So now I think it is clear that when the maximum and the minimum of the numbers are not known, the strategy in the posted solution is considered to be the best strategy.
re(6): regarding posted solution
