Techniques of Problem Solving
by Steven G. Krantz
PROBLEM 3.4.1 A hat is filled with 100 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 100). 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 100 slips - is to blindly pull slips from the hat one by one. The person looks at each slip, then either agrees to accept that number of dollars and quit the game or decides to go on and choose another slip.⏎⇥ Note that the contestant looks at each slip as he/she proceeds, and then decides whether to quit or to go on. He/she can go forward, but cannot go back. If no choice is made by the time the 100th slip is reached, then the contestant must accept the number of dollars on the 100th slip.⏎⇥ What is the best strategy for the contestant? [Here "best strategy" means that the contestant will garner the greatest number of dollars.]🏁
Submitted by zero - 02/25/2026
Academia Educational 6.07 Ranked
Global Leaderboard
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Techniques of Problem Solving
by Steven G. Krantz
PROBLEM 3.4.1 A hat is filled with 100 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 100). 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 100 slips - is to blindly pull slips from the hat one by one. The person looks at each slip, then either agrees to accept that number of dollars and quit the game or decides to go on and choose another slip.⏎⇥ Note that the contestant looks at each slip as he/she proceeds, and then decides whether to quit or to go on. He/she can go forward, but cannot go back. If no choice is made by the time the 100th slip is reached, then the contestant must accept the number of dollars on the 100th slip.⏎⇥ What is the best strategy for the contestant? [Here "best strategy" means that the contestant will garner the greatest number of dollars.]🏁
Submitted by zero - 02/25/2026
Academia Educational 6.07 Ranked