Binary Sequence Puzzle
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From: Richard Heathfield on 30 May 2010 15:13 In <6b45d36f-6c9c-4e47-88a2-4f27ece7d357(a)42g2000prb.googlegroups.com>, James Dow Allen wrote: > On May 29, 12:35 am, Ludovicus <luir...(a)yahoo.com> wrote: >> On 28 mayo, 10:12, Leroy Quet <qqq...(a)mindspring.com> wrote: >> > What rule best determines the pattern of 0's and 1's in this >> > infinite sequence. >> . >> As a Fourier Series can determine any pattern, you must to specify >> what type of function is permissible. > > (Leroy mentioned this sort of objection in his OP.) > > One often hears similar objection to "Find the next number > in this sequence" problems, but I think it's often misapplied. > Clearly one seeks the *simplest* answer; i.e. a pattern which > can be expressed with fewer words (or perhaps, since we're > cross-posted to sci.math, less Kolmogorov complexity). > > Now *some* such puzzles may have two (or more) answers > with almost equally simple explanations. But that would > make them *more* fun, not less! Any examples? I suppose the obvious example is: 1 2 4 8 16 ? -- Richard Heathfield <http://www.cpax.org.uk> Email: -http://www. +rjh@ "Usenet is a strange place" - dmr 29 July 1999 Sig line vacant - apply within
From: Robert Israel on 30 May 2010 16:42
Richard Heathfield <rjh(a)see.sig.invalid> writes: > In <6b45d36f-6c9c-4e47-88a2-4f27ece7d357(a)42g2000prb.googlegroups.com>, > James Dow Allen wrote: > > > On May 29, 12:35 am, Ludovicus <luir...(a)yahoo.com> wrote: > >> On 28 mayo, 10:12, Leroy Quet <qqq...(a)mindspring.com> wrote: > >> > What rule best determines the pattern of 0's and 1's in this > >> > infinite sequence. > >> . > >> As a Fourier Series can determine any pattern, you must to specify > >> what type of function is permissible. > > > > (Leroy mentioned this sort of objection in his OP.) > > > > One often hears similar objection to "Find the next number > > in this sequence" problems, but I think it's often misapplied. > > Clearly one seeks the *simplest* answer; i.e. a pattern which > > can be expressed with fewer words (or perhaps, since we're > > cross-posted to sci.math, less Kolmogorov complexity). > > > > Now *some* such puzzles may have two (or more) answers > > with almost equally simple explanations. But that would > > make them *more* fun, not less! Any examples? > > I suppose the obvious example is: > > 1 2 4 8 16 ? 30 = The number of positive divisors of 6! 31 = Maximal number of regions formed by joining 6 points around a circle by straight lines 23 = 1 + 1+2+4+8+1+6 See <http://www.research.att.com/~njas/sequences/?q=1%2C+2%2C+4%2C+8%2C+16&sort=0&fmt=0&language=english&go=Search> -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |