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(3): the solution by pleasance)
No apologies please pleasance but I think that even I am facing problems in explaining things to you as well as Cory. My proof is based on what you have mentioned in your comment pleasance (the case of unlimited integers, that is, when we do not know what is the maximum of all the integers written on the slips) and also the probabilities are changing as I have shown in my proof that the probability of the event that the slip with a number greater than the maximum observed among the first 'k' rejected depends on 'k' thus showing that the probabilities are not the same.
Apologies from my part too if I am not able to explain you properly exactly what is happening in the problem.
let's wait in that case for someone who would be able to explain in simple words and explanation the entire thing.
Sorry again :(
re(4): the solution
