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).
Ravi,
I read the solution with interest, and it is indeed a good, well written proof. However, I don't think it addresses the problems of an infinite distribution nor the suggestion of a presumed maximum likely number.
Perhaps the question needs a slight amendment? For example, if the slips could have any real number between 0 and 1 million, this strategy is definitely valid. One could make it grams of gold rather than rupees, for instance, for a more 'continuous' prize. The strategy might need a small amendment for the case of just a few slips, where the first was near the maximum, but now I'm getting petty.
re: the solution
