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(4): regarding posted solution by Charlie)

Thanks Charlie. Now I understand exactly what Cory was trying to say but I think this has already been commented by someone (I do not remember exactly who) that the solution that has been put up by me, that is, the strategy that I am applying is used when the maximum of the numbers is not known and we know nothing about the distribution of the numbers except for this that they are distinct positive integers and therefore has a maximum.
And what you have explained in your comment is the one in which we know the minimum and the maximum of the numbers. I mean the ranges in which they lie (not exactly the minimum and the maximum among them, which is quite obvious).

Posted by Ravi Raja on 2003-03-28 19:10:26