Make Puzzles Great Again

Nicolás Aristizabal (1) , Carlos Pinzón (1) , Camilo Rueda (2, 1) , Frank D. Valencia (3, 2)

1 Pontificia universidad Javeriana, Cali
2 AVISPA Resarch Group - Ambientes VISuales de Progamación Aplicativa
3 COMETE - Concurrency, Mobility and Transactions

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.

Mots clés: hat problems; mathematical puzzles; recreational mathematics

Domaines: Combinatoire [math.CO]; Mathématiques générales [math.GM]; Informatique et théorie des jeux [cs.GT]

Nicolás Aristizabal, Carlos Pinzón, Camilo Rueda, Frank D. Valencia. Make Puzzles Great Again. Mário S. Alvim; Konstantinos Chatzikokolakis; Carlos Olarte; Frank Valencia. The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy - Essays Dedicated to Catuscia Palamidessi on the Occasion of Her 60th Birthday, 11760, Springer, pp.442-459, 2019, Lecture Notes in Computer Science, 978-3-030-31174-2. ⟨10.1007/978-3-030-31175-9_25⟩. ⟨hal-02410767⟩