The MinptitleM Game

Description
To an adult, it’s obvious that the day of someone’s death is not precisely determined by the day of birth, but it’s a very different story for a child. When the third named author was four years old he asked his father, the fifth named author: If two people are born on the same day, do they die on the same day? While this could easily be demonstrated through murder, such a proof would greatly diminish the possibility of teaching additional lessons, and thus a different approach was taken. With the help of the fourth named author they invented what we’ll call the MinpabsM Game: Given k people, each simultaneously flips a fair coin, with each eating an MinpabsM on a head and not eating on a tail. The process then continues until all MinpabsM’S are consumed, and two people are deemed to die at the same time if they run out of MinpabsM’S together1 . This led to a great concrete demonstration of randomness appropriate for little kids; it also led to a host of math problems which have been used in probability classes and math competitions. There are many ways to determine the probability of a tie, which allow us in this article to use this problem as a springboard to a lot of great mathematics, including memoryless process, combinatorics, statistical inference, graph theory, and hypergeometric functions.

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ID Label Size Mimetype Created
OBJ OBJ datastream 426.08 KiB application/pdf 2020-06-15
TN TN 2.49 KiB image/jpeg 2020-06-15