Logical Puzzles

This type of puzzles can be solved using reified constraints, i.e., constraints over variables that are restricted to a domain of 0 and 1, expressing logical values. Special propagators for reified constraints which express the usual connectives like disjunction etc. are available.

  • The Zebra Puzzle
  • Who's "ploemp"?
  • The birthday
  • Abians and Bebians
  • Kalotan males and females
  • The Self-Referential Aptitude Test (SRAT pages of Martin Henz)
  • The Zebra Puzzle From the Oz Primer

    Five men with different nationalities live in the first five houses of the street. There are only houses on one side of the street. The men practice different professions, and each of them has a favorite drink and a favorite animal, all of them different. The five houses are painted in different colours. The following facts are known:

    • The Englishman lives in a red house.
    • The Spaniard owns a dog.
    • The Japanese is a painter.
    • The Italian drinks tea.
    • The Norwegian lives in the first house.
    • The owner of the green house drinks coffee.
    • The green house comes after the white one.
    • The sculptor breeds snails.
    • The diplomat lives in the yellow house.
    • Milk is drunk in the third house.
    • The Norwegian's house is next to the blue one.
    • The violinist drinks juice.
    • The fox is in the house next to that of the doctor.
    • The horse is in the house next to that of the diplomat.
    • The zebra is in the white house.
    • One of the men drinks water.

    Who lives where?

    Who's "ploemp"? From the Zeit Magazine

    "Who's ploemp and who isn't?" asks the soolic Typher, while palampling nervously at his lopperdumpy.

    "I've explained it to you a hundred times already", replies the Heltzpusine cooly, "but because you can quotsh so beautifully in the slicksy hulk, I'clarofy it once more".

    The Heltzpusine spoke then:

    "If the Arpus is ploemp and at the same time neither the Flutz nor the Gnutz, then the Ol'Jauze isn't ploemp. If of the brothers Gnutz and Arpus at least one is ploemp, then the dumb Blondo is ploemp, but not the Hockerprotz. If the Flutz is ploemp, then the dumb Blondo is, too, but to the contrary, the Drulf not. If the Drulf isn't ploemp, then the Ol'Jauze is, surely; but the Gnutz is not ploemp if the Ol'Jauze is. If the Ebradulp is ploemp, then inevitably the Drulf is ploemp. And if the Arpus is not ploemp, then the Drulf cannot be. If the Ol'Jauze is ploemp, then so the Hockerprotz! Additionally, if the Ebradulp isn't ploemp, so on the one side, the Ol'Jauze isn't ploemp, but then the Gnutz is."

    The soolic Typer was quite impressed by this sermon. Close to tears, he thanked the Heltzpusine with the words:

    "Loveloy Heltzpusine! There's nothing like a clear, unpretentious explanation. I'll never forget again who's ploemp and who isn't"


    The birthday modified from a prolog lecture by Espen Vestre, summer 1993

    Zorgon met Nuq the other day. "Wok's Twin-Twins have birthday tomorrow", he said. "And Wok invented four presents for them, but can't decide who's getting what. He made a screaming sack, a rolling rock, an idiot incinerator and a some useless underwear. But he told me that at least he knew

    • if Abba gets the incinerator, Bobbo would get the sack and Drit the rock. If he got the rock, Bobbo would receive the underwear and Drit the incinerator. If he gave him the sack, then Carson would be facing the underwear and Drit the rock. Otherwise, Bobbo would have the incinerator and Carson the sack.
    • However, if he gave Bobbo the rock, Abba would get the sack and Carson the underwear. Or, if he decided to give him the sack, he'd see Abba with the underwear and Drit with the rock.
    • Carson getting the sack would imply Drit getting the incinerator. If he got the underwear instead, Bobbo would have to do with the incinerator and Abba with the rock.
    • The thing he was most sure of was that he wouldn't give Drit the underwear without giving the incinerator to Abba and the sack to Bobbo.
    "Ah, don't believe him", said Nuq, "I have good sources informing me that he is never telling the truth to anyone".

    "You should change your sources", said Zorgon. "They are obviously lying".

    What are the Twin-Twins getting if Wok is actually telling the truth?

    And what's wrong with the information that Wok is a consequent liar?

    Abians and Bebians From the Zeit Magazine, 28/1996

    A while ago, I was visitor at the knusic minister president. He introduced me to the other guests, seven members of the knusic parliament. He told me:

    "Every one of these lords of parliament is either an Abian or a Bebian, but who comes from which tribe, you'll have to find out for yourself"

    Like everyone should know nowadays, Abians always tell the truth, while any assertion stated by a Bebian is wrong. So I asked the delegates about their tribal ties.

    Nose-Knosi: "If Nese-Knesi is Bebian, then either Nay-Knasi or Noy-Knosi is Abian". Nese-Knesi: "If Nose-Knosi is one of the Abians, then Noy-Knosi is Bebian, being the case that Nise-Knisi is Abian". Nise-Knisi: "Nuse-Knusi is from the same tribe as Nay-Knasi". Nose-Knosi: "If Noy-Knosi is Bebian, then Nase-Knasi is Abian". Nuse-Knusi: "I am Abian, but Nose-Knosi is Bebian: Nay-Knasi: ĻIf Nuse-Knusi is Bebian, so Nose-Knosi Abian" Noy-Knose: "Either Nase-Knasi or Nay-Knasi is Abian"

    The minister, who was an Abian (by the way), was very amused by the interviews he had witnessed and remarked: "You can deduce precisely who is Abian and who is Bebian from what they said".

    Kalotan males and females found by Dorai Sitaram (dorai@cs.rice.edu)

    Kalotan males always tell the truth. Kalotan females never make two consecutive true or untrue statements (i.e., they lie and tell the truth in strict alteration). An anthropologist who doesn't know Kalotan meets a Kalotan (heterosexual) couple and their child Kibi. He asks Kibi: "Are you a boy?". Kibi answers in Kalotan, which the anthropologist does not get.

    The anthropologist turns to the parents for explanation. One of them says: "Kibi said, 'I am a boy'". The other adds: "Kibi is a girl. Kibi lied."

    Solve for the sex of the parents (i.e., which parent made which statement) and Kibi.

    Markus Löckelt