Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site emacs.UUCP Path: utzoo!watmath!clyde!burl!ulysses!bellcore!decvax!cca!emacs!pz From: pz@emacs.UUCP (Paul Czarnecki) Newsgroups: net.puzzle Subject: Re: A "logic puzzle" Message-ID: <8@emacs.UUCP> Date: Thu, 30-Jan-86 08:47:36 EST Article-I.D.: emacs.8 Posted: Thu Jan 30 08:47:36 1986 Date-Received: Sat, 1-Feb-86 05:46:41 EST References: <292@watdragon.UUCP> <2578@pucc-h> Reply-To: pz@eno.UUCP (Paul Czarnecki) Distribution: net Organization: Uniworks Inc., Wellesley, MA Lines: 68 Summary: the answer In article <2578@pucc-h> ags@pucc-h.UUCP (Dave Seaman) writes: [Dave corrects the previous poster...] >The first asks "How old are they?", to which the second replies > > "The sum of their ages is thirteen, and the product of their > ages is equal to your age." > >The first says, "I can't tell their ages from that." >The second adds, "The oldest weighs 61 pounds." > >The first says, "Now I know their ages." > >Dave Seaman pur-ee!pucc-h!ags *** SPOILER WARNING *** *** answer follows *** When I first saw this problem I thought is was impossible. I also thought that I had to apply some *reasonable* constraints. Well, after looking at some of the other solutions posted so far I realized that everybody so far has been making one BIG mistake. And you only have to apply one real life constraint. You see, the first friend *knows* his own age! (we however don't know it, yet) a exhaustive search yields: kids' friend's ages age 1 1 11 11 ; *maybe* we can throw this one out! 1 2 10 20 ; okay, so he was precocious 1 3 9 27 1 4 8 32 1 5 7 35 1 6 6 36 2 2 9 36 2 3 8 48 2 4 7 56 2 5 6 60 3 3 7 63 3 4 6 72 ; somewhere here we *maybe* could start 3 5 5 75 ; throwing things away. But I really don't 4 4 5 80 ; want the AARP and Dr. Ruth down my back. since friend1 knows his own age and he *still* can't decide we know the the answer must be one of: 1 6 6 36 2 2 9 36 Nows here's the part I don't like in a logic puzzle, a 6 year old is more likely to weigh 61 pounds than a 9 year old is. (is this true? I don't know!) therefore the answer is 1 6 6. pZ -- -- You pretend I'm him and I'll pretend you're her. Paul Czarnecki Uniworks, Inc. decvax!{cca,wanginst!infinet}!emacs!pz 20 William Street emacs!pz@cca-unix.ARPA Wellesley, MA 02181 (617) 235-2600