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)
Cory you had once mentioned in your own comment that: "....Of course this requires that all the numbers are distinct (i.e. there are no repeats), and positive (if zero were allowed then the largest slip could be n-1), and that the player knew those facts", but here the person does not know that what the highest number is on the slips. So how can he conclude that the largest slip could be (N-1), since it is always possible that the minimum number among the slips is, say, (N + 1).
Someone has also commented that the strategy that I am using is valid if the person has no idea of the distribution of the numbers and therefore does not know what is the maximum and the minimum values in the given slips. I do not remember who but I'll post it as soon I I find it out.
re(6): regarding posted solution
