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: regarding posted solution by Ravi Raja)
Ravi, this was a special case solution amendment, not something I was considering as a general case. To expand;
say that there are 20 slips (okay "that there are 20 slips" he he), which means that the stategy is to look at the first 7 or 8 slips to find the number you're lloking to exceed.
For the ease of demonstration, I'll assume that the numbers on the slips (which according to the problem are all distinct and positive (i.e. no zero)) begin at 3 and include every integer from there up to 22. Of course this is no more likely than any other arrangement of numbers, but this example can be expanded to use when necessary. On with the scenario...
In the first 8 slips, the highest number seen could be as low as 10, and is fairly likely to be less than 20. In this case, rather than looking for the first number higher than 10 (or whatever it was), the player may, because he knows that one slip must have at least "n", look for the first slip of n or greater, bettering his outcome from looking for the first slip above 8 (or whatever)
Did my explanation make more sense this time?
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.
re(2): regarding posted solution
