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The Josephus Problem
This simple web page leads students on an exploration of the "Josephus Problem," a classic problem of recreational mathematics involving the elimination of people arranged in a circle by, one at a time, removing every kth remaining person until only one person is left. The page offers a simple interface where a student or instructor enters the number of people in the circle to start the "game" and the number k specifying how they will be eliminated. The program produces the entire elimination order of the people using these parameters. The student activities on the site ask questions that can be explored using the program, including questions to get students to make the transition from seeing a pattern to explaining the pattern using recursive reasoning.
The author suggests that this resource should be used by students to explore recursive reasoning at the beginning of a discrete mathematics course, but it is not clear how this will work if the class does not meet in a common area with computers. It could still be effective if used by the students outside of class, but it would probably require more direction from the instructor in this case.
The page provides background information and a guide for instructors, in addition to the list of activities for students using this resource. This is a nice example of a simple browser-based application to promote active learing through exploration.
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