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wu :: forums    riddles    easy (Moderators: Grimbal, Icarus, towr, SMQ, ThudnBlunder, william wu, Eigenray)    Factorial Product « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Factorial Product  (Read 383 times) Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Factorial Product   « on: Mar 7th, 2004, 4:26am » Quote Modify Given that a,b,c,d[in][bbn], and a<b<c, solve a!*b! = c!. Prove that the solution is unique.   What about a!*b!*c! = d! ? IP Logged mathschallenge.net / projecteuler.net Barukh Uberpuzzler     Gender: Posts: 2276 Re: Factorial Product   « Reply #1 on: Mar 7th, 2004, 7:49am » Quote Modify on Mar 7th, 2004, 4:26am, Sir Col wrote: Given that a,b,c,d[in][bbn], and a<b<c, solve a!*b! = c!. I think a, b = a! - 1, c = a! would do.   Quote: Prove that the solution is unique. ??   IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Factorial Product   « Reply #2 on: Mar 7th, 2004, 8:00am » Quote Modify I was gonna say that.. but I'm too slow today     just to contribute at least something, :: a > 2, else a<b<c won't hold if c=a! and b=c-1 :: « Last Edit: Mar 7th, 2004, 8:04am by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Factorial Product   « Reply #3 on: Mar 7th, 2004, 8:32am » Quote Modify Dang! I missed that trivial case, but good spot you two. Obviously if b=c–1, a!=c!/b!=c.   Okay, a new restriction... a<b<c–1.   Now go prove the existence of the unique solution...   IP Logged mathschallenge.net / projecteuler.net towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Factorial Product   « Reply #4 on: Mar 7th, 2004, 3:08pm » Quote Modify I found one solution, whether it's the only one, I can't prove yet.. :: 6!*7!=10! :: IP Logged Wikipedia, Google, Mathworld, Integer sequence DB KarmaBandit Newbie     Gender: Posts: 16 Re: Factorial Product   « Reply #5 on: Mar 7th, 2004, 4:39pm » Quote Modify Here's Mathworld's input: http://mathworld.wolfram.com/FactorialProducts.html   16! = 14! 5! 2! 10! = 7! 5! 3! = 7! 6!   It looks like mathworld doesn't know of any uniqueness proof, either. That's my signal to give up! IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Factorial Product   « Reply #6 on: Mar 8th, 2004, 12:01am » Quote Modify on Mar 7th, 2004, 8:32am, Sir Col wrote: Okay, a new restriction... a<b<c–1.   Now go prove the existence of the unique solution...   It seems that towr's solution may be the unique one. However, credible sources (including KarmaBandit's link) tell me that the proof is far beyond the scope of the easy section.     So, Sir Col, if you've got the proof I would definitely like to see it! IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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