wall@fortune.UUCP (Jim Wall) (10/26/83)
This comes from the latest 'Discover' magazine, my kind of puzzle. A census taker comes to a persons house and asks him the age of his three daughters. The man replies that the product of their ages (whole numbers only) is 72. And that the sum of their ages is his house number. The census taker replied that this wasn't enough information to solve the problem. In that case, the man of the house said, the eldest loves chocolate milk. What are the ages of the three girls? -Jim Solution to follow in a few days....
cjp@vax135.UUCP (10/27/83)
This is a trick question, right? The answer is (rot 13 to prevent spoiler): Gur qnhtugref ner fraragl-gjb, bar, naq bar. Gur pubpbyngr zvyx vf sbe fbbguvat gur ryqrfg qnhtugre'f hypref. Gur gjvaf ner gur erfhyg bs gur thl'f jvsr univat gb hfr sregvyvgl qehtf gb trg certanag ng gur ntr bs 90 be fb. Gur ersrerapr gb gur ubhfr ahzore vf gur erfhyg bs gur thl orvat fravyr. Ur npghnyyl yvirf ng ahzore 42. :i) Everything makes sense, Charles Poirier
jay@rochester.UUCP (Jay Weber) (10/28/83)
Excuse me if I'm missing something, but you still don't have enough
information to figure out the ages. Did you forget to give the house
number? I can think of two solutions: (2 * 2 * 18) = (2 * 4 * 9) = 72.
-Jay Weber
{..!seismo!rochester!jay, jay@rochester.arpa}gawilson@watdragon.UUCP (Graham Wilson) (02/22/86)
I have read the last two or three hundred articles in new.puzzle, and I have not seen this one (or any variations). Credit goes to me (Graham Wilson) and Peter Fruchter. We originally thought it up as an analogy to explain Godel's Incompleteness Theorem... Consider a machine which is used to create true sentences (for example, the sentence "A dog is a dog" is true). If the machine is "complete", then it could, given time, produce the set of ALL true sentences. If the machine is "consistent", then all the sentences that it produces will be true. Question: Can such a machine exist (even in theory)? Note that your answer must involve an iron-clad proof (i.e. like a math theorem. Persons who have read "Godel, Escher, Bach, An...." by D.H. should consider disqualifying themselves. --------------------------------------------------------------------------- Graham Wilson University of Waterloo gawilson@watdragon
ags@pucc-h (Dave Seaman) (02/24/86)
In article <423@watdragon.UUCP> gawilson@watdragon.UUCP (Graham Wilson) writes: >Consider a machine which is used to create true sentences (for example, >the sentence "A dog is a dog" is true). If the machine is "complete", >then it could, given time, produce the set of ALL true sentences. If the ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >machine is "consistent", then all the sentences that it produces will be >true. > >Question: Can such a machine exist (even in theory)? The machine cannot produce the set of ALL true sentences unless that set is finite. I think you meant to say any given true sentence would eventually be produced by the machine. -- Dave Seaman pur-ee!pucc-h!ags
gawilson@watdragon.UUCP (Graham Wilson) (02/28/86)
With respect to the puzzle I recently submitted concerning the Sentence-producing machine, there is something I wish to clarify: The comment that the machine is complete if, given time, it could produce all true sentences should have been the machine is complete if there does not exist a true sentence which the machine could not produce. The original wording presents a problem if the number of true sentences is uncountably infinite (there is no problem if the # is countably infinite). My thanks to Rico Mariani for pointing this out. Sorry for the inconvenience. Graham Wilson gawilson@watdragon
ags@pucc-h (Dave Seaman) (02/28/86)
In article <478@watdragon.UUCP> gawilson@watdragon.UUCP (Graham Wilson) writes: >With respect to the puzzle I recently submitted concerning the >Sentence-producing machine, there is something I wish to clarify: > >The comment that the machine is complete if, given time, it could >produce all true sentences should have been the machine is complete >if there does not exist a true sentence which the machine could not >produce. The original wording presents a problem if the number of >true sentences is uncountably infinite (there is no problem if the ># is countably infinite). There is no chance that the number of true sentences can be uncountable, since there are are only countably many sentences, regardless of truth value. There are only finitely many sentences of length N, for each N. The number of sentences which can be produced by the machine in any given time is finite. If there are infinitely many true sentences, the best you can say is that any given true sentence is eventually produced by the machine. There is never a time when all true sentences have been produced. -- Dave Seaman pur-ee!pucc-h!ags