Abstract
We present original solutions to four challenging mathematical puzzles. The first two are concerned with random processes. The first, here called The President’s Welfare Plan, can be reduced to computing, for arbitrary large values of n, the expected number of iterations of a program that increases a variable at random between 1 and n until exceeds n. The second one, called The Dining Researchers, can be reduced to determining the probability of reaching a given point after visiting all the others in a circular random walk. The other two problems, called Students vs Professor and Students vs Professor II, involve finding optimal winning group strategies in guessing games.
This work have been partially supported by the ECOS-NORD project FACTS (C19M03) and the Colciencias project CLASSIC (125171250031).
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Notes
- 1.
It would seem that in real life this kind of plan is often implemented except that the random amounts of money are not uniformly chosen and often include 0.
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Acknowledgements
We would like to thank Thomas Given-Wilson and Bartek Klin for bringing the third and fourth puzzles to our attention.
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Aristizabal, N., Pinzón, C., Rueda, C., Valencia, F. (2019). Make Puzzles Great Again. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_25
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