Abstract
An evil warden is in charge of 100 prisoners (all with different names). He puts a row of 100 boxes in a room. Inside each box is the name of a different prisoner. The prisoners enter the room one at a time. Each prisoner must open 50 of the boxes, one at a time. If any of the prisoners does not see his or her own name, then they are all killed. The prisoners may have a discussion before the first prisoner enters the room with the boxes, but after that there is no further communication. A prisoner may not leave a message of any kind for another prisoner. In particular, all the boxes are shut once a prisoner leaves the room. If all the prisoners choose 50 boxes at random, then each has a success probability of 1/2, so the probability that they are not killed is 2−100, not such good odds. Is there a strategy that will increase the chances of success? What is the best strategy?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L. Babai, P. Frankl, Linear Algebra Methods in Combinatorics, preliminary version 2 (1992), 216 pp.
E.R. Berlekamp, On subsets with intersections of even cardinality. Can. Math. Bull. 12, 363–366 (1969)
R.C. Bose, A note on Fisher’s inequality for balanced incomplete block designs. Ann. Math. Stat. 619–620 (1949)
W. Bruns, J. Gubeladze, Polytopes, Rings, and K-Theory (Springer, Dordrecht, 2009)
Y. Caro, Simple proofs to three parity theorems. Ars Combin. 42, 175–180 (1996)
E. Curtin, M. Warshauer, The locker puzzle. Math. Intelligencer 28, 28–31 (2006)
R.A. Fisher, An examination of the different possible solutions of a problem in incomplete blocks. Ann. Eugen. 10, 52–75 (1940)
A. Gál, P.B. Miltersen, The cell probe complexity of succinct data structures, in Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP) (2003), pp. 332–344
P. Gordan, Über die Auflosung linearer Gleichungen mit reellen Coefficienten. Math. Ann. 6, 23–28 (1873)
R.L. Graham, H.O. Pollak, On the addressing problem for loop switching. Bell Syst. Tech. J. 50, 2495–2519 (1971)
R.L. Graham, H.O. Pollak, On embedding graphs in squashed cubes, in Lecture Notes in Mathematics, vol. 303 (Springer, New York, 1973), pp. 99-110
K.H. Leung, B. Schmidt, New restrictions on possible orders of circulant Hadamard matrices. Designs Codes Cryptogr. 64, 143–151 (2012)
J. Matoušek, Thirty-Three Miniatures (American Mathematical Society, Providence, 2010)
H.J. Ryser, Combinatorial Mathematics (Mathematical Association of America, Washington, 1963)
R. Stanley, Differentiably finite power series. Eur. J. Combin. 1, 175–188 (1980)
R. Stanley, Enumerative Combinatorics, vol. 2 (Cambridge University Press, New York, 1999)
K. Sutner, Linear cellular automata and the Garden-of-Eden. Math. Intelligencer 11, 49–53 (1989)
R.J. Turyn, Character sums and difference sets. Pac. J. Math. 15, 319–346 (1965)
R.J. Turyn, Sequences with small correlation, in Error Correcting Codes, ed. by H.B. Mann (Wiley, New York, 1969), pp. 195–228
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Stanley, R.P. (2018). Miscellaneous Gems of Algebraic Combinatorics. In: Algebraic Combinatorics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77173-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-77173-1_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77172-4
Online ISBN: 978-3-319-77173-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)