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).
I believe there's a problem here: we don't know the probability distribution of numbers appearing on the slips of paper. I know that in logic problems we generally ignore trivialities such as, "that number is so large, it's more than there are atoms in the universe, let alone rupees you can give someone". But in this case, it's more than logistics. It's simply NOT POSSIBLE to have an even distribution for ANY positive integer between 1 and infinity. In other words: some numbers are more likely than others.
If I'm not mistaken, this must be taken into account before attempting any strategy as those suggested by Cory and Charlie. For example, we can estimate the largest likely number that can appear on the slips. Let's say N=2. If we decide that sums larger than 1,000,000,000 rupees are highly unlikely, we might decide to keep the first slip if it says 900,000,000, but to take the second one if the first says 134. The largest estimated number is not the point: assessing the distribution is.
What's the distribution?
