Number Representation Problem
in [Math]
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From: Charlie-Boo on 24 Jan 2010 10:03 How can I map an integer N between 1 and 1,000,000 to a string f(N) of 12 letters where I can map back from f(N) to N, and f(N+1) bears no resemblance to f(N)? (Better yet f(N+m) bears no resemblance to f(N) for m=1 to 1000 or f(m) for any m not equal to N.) C-B
From: TCL on 24 Jan 2010 11:35 On Jan 24, 10:03 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > How can I map an integer N between 1 and 1,000,000 to a string f(N) of > 12 letters where I can map back from f(N) to N, and f(N+1) bears no > resemblance to f(N)? (Better yet f(N+m) bears no resemblance to f(N) > for m=1 to 1000 or f(m) for any m not equal to N.) > > C-B What is the limitation on the length of the strings? If there is none, then there is a trivial answer to your question. -TCL
From: hagman on 24 Jan 2010 12:24 On 24 Jan., 17:35, TCL <tl...(a)cox.net> wrote: > On Jan 24, 10:03 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > > > How can I map an integer N between 1 and 1,000,000 to a string f(N) of > > 12 letters where I can map back from f(N) to N, and f(N+1) bears no > > resemblance to f(N)? (Better yet f(N+m) bears no resemblance to f(N) > > for m=1 to 1000 or f(m) for any m not equal to N.) > > > C-B > > What is the limitation on the length of the strings? If there is none, > then there is a trivial answer to your question. > -TCL Prepare a table of 1000000 "random" strings
From: HallsofIvy on 24 Jan 2010 02:30 > On Jan 24, 10:03 am, Charlie-Boo > <shymath...(a)gmail.com> wrote: > > How can I map an integer N between 1 and 1,000,000 > to a string f(N) of > > 12 letters where I can map back from f(N) to N, and > f(N+1) bears no > > resemblance to f(N)? (Better yet f(N+m) bears no > resemblance to f(N) > > for m=1 to 1000 or f(m) for any m not equal to N.) > > > > C-B > > What is the limitation on the length of the strings? > If there is none, > then there is a trivial answer to your question. > -TCL He DID say "strings of 12 letters". I interpreted that to me the length of the string is 12. I guess you could take it to me any string from an alphabet of 12 letters.
From: TCL on 24 Jan 2010 15:10
On Jan 24, 12:30 pm, HallsofIvy <GeorgeI...(a)netzero.com> wrote: > > On Jan 24, 10:03 am, Charlie-Boo > > <shymath...(a)gmail.com> wrote: > > > How can I map an integer N between 1 and 1,000,000 > > to a string f(N) of > > > 12 letters where I can map back from f(N) to N, and > > f(N+1) bears no > > > resemblance to f(N)? (Better yet f(N+m) bears no > > resemblance to f(N) > > > for m=1 to 1000 or f(m) for any m not equal to N.) > > > > C-B > > > What is the limitation on the length of the strings? > > If there is none, > > then there is a trivial answer to your question. > > -TCL > > He DID say "strings of 12 letters". I interpreted that to me the length of the string is 12. I guess you could take it to me any string from an alphabet of 12 letters.- Hide quoted text - > > - Show quoted text - If that is what OP meant, then order the strings in dictionary (lexicographic) order. Say the letters are a,b,c,...,l. Then define f(1)= the first in the order = aaaaaaaaaaaa f(2)= the second in the order = aaaaaaaaaaab ...... That is a one-to-one map. -TCL |