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Full-Text Articles in Physical Sciences and Mathematics
On Passing The Buck, Adam J. Hammett, Anna Joy Yang
On Passing The Buck, Adam J. Hammett, Anna Joy Yang
The Research and Scholarship Symposium (2013-2019)
Imagine there are n>1 people seated around a table, and person S starts with a fair coin they will flip to decide whom to hand the coin next -- if "heads" they pass right, and if "tails" they pass left. This process continues until all people at the table have "touched" the coin. Curiously, it turns out that all people seated at the table other than S have the same probability 1/(n-1) of being last to touch the coin. In fact, Lovasz and Winkler ("A note on the last new vertex visited by a random walk," J. Graph Theory, …
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 …
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
The Research and Scholarship Symposium (2013-2019)
Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.
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 …