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wu :: forums    riddles    easy (Moderators: Eigenray, william wu, SMQ, Icarus, Grimbal, towr, ThudnBlunder)    100th number in sequence « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: 100th number in sequence  (Read 4878 times) Aryabhatta Uberpuzzler     Gender: Posts: 1321 100th number in sequence   « on: Jun 16th, 2007, 9:40am » Quote Modify Consider the sequence 1, 3, 4, 9, 10 ...   which is such that each number is either a power of 3 or the sum of distinct powers of 3. The numbers are arranged in increasing order.   Without using a computer/calculator, find the 100th number of this sequence. IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: 100th number in sequence   « Reply #1 on: Jun 16th, 2007, 9:56am » Quote Modify Can I write the number in base 3, for added difficulty?   IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: 100th number in sequence   « Reply #2 on: Jun 16th, 2007, 10:19am » Quote Modify IP Logged thecuriousone Newbie     Gender: Posts: 9 Re: 100th number in sequence   « Reply #3 on: Jun 16th, 2007, 12:02pm » Quote Modify hidden: is it 981?     This is what I observed:   (2^0)th term = 1st term =  (3^0) (2^1)th term = 2nd term = (3^1) (2^2) term = 4th term = (3^2) similarly (2^6)th term = 64th term = (3^6) = 729 add (2^5)th term to the above = 729 + 243 add 4th term to the above = 729 + 243 + 9   regards, thecuriousone IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: 100th number in sequence   « Reply #4 on: Jun 16th, 2007, 8:23pm » Quote Modify You got the right answer, thecuriousone.   Welcome to the forums! IP Logged thecuriousone Newbie     Gender: Posts: 9 Re: 100th number in sequence   « Reply #5 on: Jun 17th, 2007, 2:15am » Quote Modify Thanks, Aryabhatta!   But I am sure, you have a more elegant solution than what I wrote. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: 100th number in sequence   « Reply #6 on: Jun 17th, 2007, 7:06am » Quote Modify on Jun 17th, 2007, 2:15am, thecuriousone wrote: But I am sure, you have a more elegant solution than what I wrote. I'm pretty sure that what he had in mind is basicly the same.     Write 100 as binary, 100=64+32+4 = 26+25+22 = 11001002 (the subscript 2 is to denote it is in base 2, or binary). Next interpret this numberstring as a number in base 3, 11001003 = 36+35+32 = 729 + 243 + 9 = 981.   This is essentially what you're doing. Even though you don't explicitly resort to binary. Recognizing the intermediate step as binary makes it a bit simpler if you're well-versed in dealing with other number bases. Which is why Grimbal wanted to write the answer in base 3, then you don't need the last step converting it to decimal IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: 100th number in sequence   « Reply #7 on: Jun 19th, 2007, 1:44am » Quote Modify towr is right. The basic idea is the same, the presentation differs. 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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