The Complexity of Solitaire

  • Luc Longpré
  • Pierre McKenzie
Conference paper

DOI: 10.1007/978-3-540-74456-6_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)
Cite this paper as:
Longpré L., McKenzie P. (2007) The Complexity of Solitaire. In: Kučera L., Kučera A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg


Klondike is the well-known 52-card Solitaire game available on almost every computer. The problem of determining whether an n-card Klondike initial configuration can lead to a win is shown NP-complete. The problem remains NP-complete when only three suits are allowed instead of the usual four. When only two suits of opposite color are available, the problem is shown NL-hard. When the only two suits have the same color, two restrictions are shown in AC0 and in NL respectively. When a single suit is allowed, the problem drops in complexity down to AC0[3], that is, the problem is solvable by a family of constant depth unbounded fan-in {and, or, mod3}-circuits. Other cases are studied: for example, “no King” variant with an arbitrary number of suits of the same color and with an empty “pile” is NL-complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Luc Longpré
    • 1
  • Pierre McKenzie
    • 2
  1. 1.University of Texas at El Paso 
  2. 2.Université de Montréal 

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