Make Puzzles Great Again

  • Nicolás Aristizabal
  • Carlos Pinzón
  • Camilo Rueda
  • Frank ValenciaEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


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.



We would like to thank Thomas Given-Wilson and Bartek Klin for bringing the third and fourth puzzles to our attention.


  1. 1.
    Ebert, T.: Applications of recursive operators to randomness and complexity. Ph.D. thesis, University of California, Santa Barbara (1998)Google Scholar
  2. 2.
    Euler, L.: Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8, 128–140 (1736)Google Scholar
  3. 3.
    Feller, W.: An Introduction to Probability Theory and Its Applications, 2nd edn. Wiley, Hoboken (1971)zbMATHGoogle Scholar
  4. 4.
    Ferguson, T.S.: Who solved the secretary problem? Stat. Sci. 4, 282–289 (1989)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gardner, M.: Martin Gardner’s New Mathematical Diversions from Scientific American. Simon and Schuster, New York (1966)Google Scholar
  6. 6.
    Guo, W., Kasala, S., Rao, M., Tucker, B.: The Hat Problem and Some Variations, pp. 459–479. Birkhäuser, Boston (2006)zbMATHGoogle Scholar
  7. 7.
    Guy, R.K.: Unsolved Problems in Number Theory, 3rd edn. Springer, Berlin (2004). Scholar
  8. 8.
    Lagarias, J.: The Ultimate Challenge: The 3x+1 Problem. American Mathematical Society, Providence (2010)CrossRefGoogle Scholar
  9. 9.
    Ross, S.M. (ed.): Introduction to Probability Models. Academic Press, Cambridge (2007)Google Scholar
  10. 10.
    Russell, K.G.: Estimating the value of e by simulation. Am. Stat. 45, 66–68 (1991)Google Scholar
  11. 11.
    Sbihi, A.M.: Covering times for random walks on graphs. Ph.D. thesis, McGill University (1990)Google Scholar
  12. 12.
    Solov’eva, F.I.: Perfect binary codes: bounds and properties. Discrete Math. 213(1–3), 283–290 (2000)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Tao, T.: The Erdos discrepancy problem. arXiv e-prints arXiv:1509.05363 (2015)

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nicolás Aristizabal
    • 1
  • Carlos Pinzón
    • 1
  • Camilo Rueda
    • 1
  • Frank Valencia
    • 1
    • 2
    Email author
  1. 1.Pontificia Universidad Javeriana CaliCaliColombia
  2. 2.CNRS & LIX, École Polytechnique de ParisPalaiseauFrance

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