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(2): regarding posted solution by Cory Taylor)
Yes I understand what you are trying to say Cory. it is obvious that among 'N' slips with distinct positive integers, there will always exist a slip with at least a value 'N' on it or may be higher. But at the same time I have considered all the possible cases where the slip with the highest number (whatever this number be) is equally likely to be in any of the 'N' positions and if it occurs among the first 'k' which we are going to reject, then the probability of obtaining the slip with the highest number reduces to 'NIL'. So it does not matter whether we see a number higher than or lower than 'N' among the first 'k' slips. (Since here in the problem we do not know whether the numbers form a definite pattern or sequence, that is, we do not know about both the minimum and the maximum of the numbers written on the slips).
re(3): regarding posted solution
