Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Logic and Foundations
Does Logic Help Us Beat Monty Hall?, Adam J. Hammett, Nathan A. Harold, Tucker R. Rhodes
Does Logic Help Us Beat Monty Hall?, Adam J. Hammett, Nathan A. Harold, Tucker R. Rhodes
The Research and Scholarship Symposium (2013-2019)
The classical Monty Hall problem entails that a hypothetical game show contestant be presented three doors and told that behind one door is a car and behind the other two are far less appealing prizes, like goats. The contestant then picks a door, and the host (Monty) is to open a different door which contains one of the bad prizes. At this point in the game, the contestant is given the option of keeping the door she chose or changing her selection to the remaining door (since one has already been opened by Monty), after which Monty opens the chosen …
On A Multiple-Choice Guessing Game, Ryan Cushman, Adam J. Hammett
On A Multiple-Choice Guessing Game, Ryan Cushman, Adam J. Hammett
The Research and Scholarship Symposium (2013-2019)
We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability of …