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wu :: forums    riddles    hard (Moderators: ThudnBlunder, Grimbal, Icarus, towr, SMQ, Eigenray, william wu)    Evaluate f(1,000,000,000,000) « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Evaluate f(1,000,000,000,000)  (Read 696 times) pcbouhid Uberpuzzler     Gender: Posts: 647 Evaluate f(1,000,000,000,000)   « on: Nov 18th, 2005, 9:02am » Quote Modify If f(0) = 0,   and for n>0,  f(n) = n - f(f(n-1)),   what is the value of f(1,000,000,000,000)? « Last Edit: Nov 18th, 2005, 9:03am by pcbouhid » IP Logged Don´t follow me, I´m lost too. JocK Uberpuzzler     Gender: Posts: 877 Re: Evaluate f(1,000,000,000,000)   « Reply #1 on: Nov 18th, 2005, 9:49am » Quote Modify My first guess would be:   f(n) = round( phi *n + phi2/(2 + phi) ) with  round(..) denoting rounding to the nearest integer and phi = (-1+sqrt(5))/2,  the golden ratio)...   but need to think a bit further (after all, a hard problem is unlikely to be solved within an hour...   )         « Last Edit: Nov 18th, 2005, 9:52am by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Evaluate f(1,000,000,000,000)   « Reply #2 on: Nov 18th, 2005, 12:23pm » Quote Modify I remember seeing it somewhere...   Aha! It's under Strange Recursion thread. IP Logged Deedlit Senior Riddler     Posts: 476 Re: Evaluate f(1,000,000,000,000)   « Reply #3 on: Nov 26th, 2005, 3:16pm » Quote Modify on Nov 18th, 2005, 9:49am, JocK wrote: My first guess would be:   f(n) = round( phi *n + phi2/(2 + phi) ) with  round(..) denoting rounding to the nearest integer and phi = (-1+sqrt(5))/2,  the golden ratio)...   but need to think a bit further (after all, a hard problem is unlikely to be solved within an hour...   )   It's actually simpler than that - it's just   f(n) = [phi (n + 1)], although I think the reciprical definition of phi is more common, in which case it's f(n) = [(n + 1) / phi] IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: Evaluate f(1,000,000,000,000)   « Reply #4 on: Nov 26th, 2005, 11:37pm » Quote Modify You're right, although for the answer it doesn't matter:   Round(618,033,988,750.041) = [618,033,988,750.513] = 618,033,988,750   IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. 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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