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James is in a room with three other people: Alice, Bob, and Spencer. Alice and Bob are married to each other, but James knows that Bob is secretly having an affair with Spencer.

James is going to announce the identity of his "baby," the person he loves the most in the whole world. He remarks, truthfully, about the occupants of the room: "Everybody loves my baby, but my baby doesn't love anybody but me."

Which person is James's baby?

To formalize definitions: we assume the love is a directional relationship P=>Q where each endpoint P and Q represents some person in the room. We allow the possibility that a person may have any number of incoming and outgoing love relationships concurrently. (So, A may love B, but B might not love A back, and A may love C while still also loving B as well.)

(I personally discovered this curiosity in The Cuckoo's Egg by Clifford Stoll, but it certainly predates that work, since the song "Everybody Loves My Baby" was written several decades prior, in 1924.)

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  • $\begingroup$ Is Spencer a female or male's first name? $\endgroup$ – Tim Oct 27 '14 at 17:54
  • $\begingroup$ @Tim I'm not sure that matters. $\endgroup$ – Set Big O Oct 27 '14 at 18:30
  • $\begingroup$ @Geobits: I ask it not because it matters. $\endgroup$ – Tim Oct 27 '14 at 18:36
  • $\begingroup$ @Tim As far as I know it's mainly a male name (at least I haven't met any females named Spencer). $\endgroup$ – Set Big O Oct 27 '14 at 18:38
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    $\begingroup$ Alice and Bob's marriage was doomed from the start. I heard they keep secrets from each other... $\endgroup$ – corsiKa Oct 27 '14 at 19:25
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James' baby is James

If everybody loves my baby, then my baby loves my baby. Since my baby don't love anybody but me, it must be me.

Anyway, it's pretty clear that it's not one of the others, since you make absolutely no distinction between them. It would just be a random guess to choose one of them. To make this more "difficult", you could give each a line of back story to distract/mislead the readers.

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  • $\begingroup$ Indeed -- the original formulation is simply predicate logic applied humorously to song lyrics; more could be done to "puzzlify" it. As you've suggested, I've added a bit of extraneous detail to the opening paragraph to disguise the question somewhat. $\endgroup$ – apsillers Oct 27 '14 at 13:56
  • $\begingroup$ I not sure about that. Alice and Bob are married. That does not mean they still love each other. (Plus, Bob is having an affair). Also, Bob and Spencer have an affair, so we can assume they do so because they love each other. I would answer Alice. (On the other hand @Geobits reasoning does work) $\endgroup$ – njzk2 Oct 27 '14 at 18:54
  • $\begingroup$ @njzk2 There can be love with/without marriage, and the same goes for affairs (lust != love). There's just nothing in the marriage/affair part that proves love or lack of it for any of the involved parties. All you really have to go on is James' statement. The rest wasn't even present in the post when I answered it. $\endgroup$ – Set Big O Oct 27 '14 at 19:03
  • $\begingroup$ Why do we have reason to believe that everybody loves James? Nothing in the post indicates that anyone has feelings toward James. $\endgroup$ – corsiKa Oct 27 '14 at 19:28
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    $\begingroup$ @corsiKa I'm afraid I may have obfuscated the original problem a little too well, then. Indeed, this answer correctly highlights that "truthfully" is the most important word in the problem (aside from the bolded statement itself); the solution can be derived from that statement, along with the agreeing fact that James does not appear to have love relationships with anyone else in the room. The bolded statement can be taken as absolute puzzle-level truth; it is provided as a quotation from one of the characters only to make it align with the original song lyric, from which the puzzle arose. $\endgroup$ – apsillers Oct 27 '14 at 19:53

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