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Muddy Children

In: One Hundred Prisoners and a Light Bulb

Author

Listed:
  • Hans van Ditmarsch

    (Université de Lorraine, LORIA, CNRS)

  • Barteld Kooi

    (University of Groningen, Faculty of Philosophy)

Abstract

A group of children has been playing outside and they are called back into the house by their father. The children gather round him. As one may imagine, some of them have become dirty from the play. In particular: they may have mud on their face. Children can only see whether other children are muddy, and not if there is any mud on their own face. All this is commonly known, and the children are, obviously, perfect logicians. Father now says: “At least one of you is muddy.” And then: “Will those who know whether they are muddy step forward.” If nobody steps forward, father keeps repeating the request. At some stage all muddy children will step forward. When will this happen if $m$ out of $k$ children in total are muddy, and why?

Suggested Citation

  • Hans van Ditmarsch & Barteld Kooi, 2015. "Muddy Children," Springer Books, in: One Hundred Prisoners and a Light Bulb, edition 127, chapter 3, pages 21-32, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16694-0_3
    DOI: 10.1007/978-3-319-16694-0_3
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