25 Aug
2020
25 Aug
'20
3:12 p.m.
I get 328...881 with some various digits between the 328 and the 881.
On Tue, Aug 25, 2020 at 11:11 AM Andy Latto <andy.latto@pobox.com> wrote:
> For those who are interested in the combinatorics half of this puzzle, but
> not in the figure-out-how-the-unix-shell-works part, here is a spoiler for
> the first half, presenting this as a problem about substitution operations
> on strings without reference to UNIX.
>
> Consider the following partial-function f operating on (some) pairs of
> strings and returning a string: (the double quotes and plus sign here are
> metanotation, and not part of the string; I've used d and s instead of
> single and double quotes to avoid confusion).
>
> f("$x", x) = x
> f("dSd", y) = f(S, y) , where S is any string not containing a d.\
> f("sSs", y) = S, where S is any string not containing an s
> f(A+B, x) = f(A, x) + f(B, x), where + denotes concatenation.
>
> Or in words, substitute the value of the variable x for the string $x.
> Quoted strings, whether single or double quoted, are copied, with the
> quotes removed, but variable substitution occurs in single quotes, but not
> in double quotes. Single quotes inside double quotes, and vice versa, are
> not nested applications of this rule: they are simply copied like any other
> character.
>
> Now define
>
> g(x) = f(x, x)
>
> The question is how many occurences of "$x" there are in g^7("ds$xsd $x
> sd$xds")
>
> where I've inserted some spaces for readability, so I suppose I need to add
> the rule
> f(" ", y) = " "
>
> I'm pretty sure this is the right translation of the puzzle from the
> language of the unix shell to the language of math, since I've verified
> that g^3("ds$xsd $x sd$xds") = 973. So I think I've solved the unix-shell
> part of the puzzle correctly, but haven't yet a clue how to solve the
> mathematica part.
>
>
>
> On Tue, Aug 25, 2020 at 11:54 AM Robin Houston <robin.houston@gmail.com>
> wrote:
>
> > Sorry, I should have explicitly specified a Bourne-type shell.
> >
> > I’ve tried it with bash, dash and zsh, all of which behave the same
> AFAICT.
> >
> > The sequence should begin: 3, 7, 37, 973, 642493; which is probably as
> far
> > as you can get experimentally.
> >
> > Cheers,
> > Robin
> >
> > On Tue, 25 Aug 2020 at 16:44, Christopher Landauer <topcycal@gmail.com>
> > wrote:
> >
> > > robin - which unix shell? sh, bash, ksh, csh tcsh, zsh, lotsa choices
> - i
> > > do know that sh barfs on it
> > > more later,
> > > chris
> > >
> > >
> > > On Tue, Aug 25, 2020 at 8:01 AM Robin Houston <robin.houston@gmail.com
> >
> > > wrote:
> > >
> > > > I posted the below puzzle to Twitter, where no one has solved it. I
> > think
> > > > it’s too hard. Although it’s a silly question, the method of solution
> > is
> > > > quite interesting IMHO.
> > > >
> > > > (The computation would be doable by hand, if one were patient and
> > > careful,
> > > > but can be done more easily and reliably by a computer.)
> > > >
> > > > I know some of you are aware of a related problem I solved a few
> years
> > > ago.
> > > > The method of solution of this one is related, but not identical.
> > > >
> > > > Cheers,
> > > > Robin
> > > >
> > > >
> > > > A Unix shell puzzle. If you were to run this script – which I don’t
> > > > recommend doing – how many occurrences of $x would appear in the
> > output?
> > > >
> > > > x=\"\'\$x\'\"\$x\'\"\$x\"\'
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > eval x=$x
> > > > echo "$x"
> > > > _______________________________________________
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> > > > math-fun@mailman.xmission.com
> > > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
> > > >
> > >
> > >
> > > --
> > > dr. christopher landauer
> > > topcy house consulting
> > > thousand oaks, california
> > > _______________________________________________
> > > math-fun mailing list
> > > math-fun@mailman.xmission.com
> > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
> > >
> > _______________________________________________
> > math-fun mailing list
> > math-fun@mailman.xmission.com
> > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
> >
>
>
> --
> Andy.Latto@pobox.com
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>
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