Re: A little puzzle.

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.programming
Subject	Re: A little puzzle.
Date	2022-11-22 11:40 +0000
Organization	A noiseless patient Spider
Message-ID	<87tu2rkyjp.fsf@bsb.me.uk> (permalink)
References	<875yf8nijb.fsf@bsb.me.uk> <tlgp7v$3sinl$1@dont-email.me> <87tu2sm2bg.fsf@bsb.me.uk> <tli0jj$25jq$1@dont-email.me>

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David Brown <david.brown@hesbynett.no> writes:

> On 21/11/2022 22:21, Ben Bacarisse wrote:
>> David Brown <david.brown@hesbynett.no> writes:
>> 
>>> On 21/11/2022 21:45, Ben Bacarisse wrote:
>>>> I wonder if there are any real posters here?  Let's see...
>>>> I came across a trivial programming task that must have been solved a
>>>> thousand times by other programmers, but it had never crossed my path
>>>> until yesterday.  I must be feeling my age because I made a real hash of
>>>> tackling it at first.  Anyway, I thought it might be of interest.
>>>> Consider any ordered measure that "wraps round" -- bearings in degrees,
>>>> minutes in the hour, indeed hours in either the 12 or 24 hour clock.
>>>> The problem is to determine if a given value is in the sub-range
>>>> specified by a start and an en value.
>>>> I was specifically concerned with integer values where the sub-range
>>>> includes the start value but excludes the end value.
>>>> Though I am not sure this merits the term "puzzle", I suggest that
>>>> solutions be posted with some spoiler protection.  Do all the news
>>>> readers used by programmers (or ex programmers) all respect the presence
>>>> of a form-feed character...
>>>> 
>>>> ... like this?  Because that's my favourite way, rather than posting
>>>> lots of dummy lines before the solution.
>>>>
>
> Thunderbird seems to respect it when showing the posts.  I am not sure of the most convenient way to add one.  I'll try copy-and-pasting your 
> FF character...
>
>>>> 
>
> Did that work?

Yes, but for my newsreader a form feed only hides what's below it when
at the start of a line.

>>> Are there any restrictions, such as sticking to integers?  The problem
>>> becomes quite difficult if your measure is the reals in [0, 1) and
>>> your "n" is, say, π/4...
>> I don't follow.  What is "my" n?  I did not mention an n.
>
> You referred to a "start value" and an "en value".

Sorry, typo.  End value.

> I like to use names, so I'll call the "start value" "a", and use "n"
> for the "en value".  So as far as I understand it, you are asking for
> a function that takes an input "x" and determines if there is an
> integer "i" such that
>
> 	x ≡ a + i.n
>
> where the congruence is over a "wrapping" set.

Hmm...  I must have made a real hash of the description (and I was being
deliberately a bit vague for reasons that should come out later) because
there is always such an i.

Here's an example.  An event starts at 5 minutes to the hour (start =
55) and ends at quarter past (end = 15).  The x's 55, 58, 3, 12 and so
on are in the range, 53, 17 and 33 are not.

The fact that all data are integers is not really material.  We could
consider compass points in [0, 2*pi) and have arbitrary start and end
bearings.

>> I don't see why the problem can't be naturally extended to a circular
>> real interval [0, 1), subject to the fact that we'll use floating point
>> numbers for practical purposes.  But I don't think this is what you were
>> talking about.
>
> Well, the point is if "being specifically concerned with integers"
> means the puzzle is limited to integer ranges, or if that is just what
> you were thinking about first.  I suppose you /do/ mean sticking to
> integers, because I'd be surprised if a solution were possible once
> you bring arbitrary real numbers into it.  That kind of mathematics
> leads to things like the Banach-Tarski paradox, and watching far too
> many maths Youtube videos...

I think I've not explained the problem well because there's not that
rarefied about it!

-- 
Ben.

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A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-21 20:45 +0000
  Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-21 22:06 +0100
    Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-21 21:21 +0000
      Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 09:17 +0100
        Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-22 11:07 +0000
          Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 15:17 +0100
        Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 11:40 +0000
          Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 15:26 +0100
            Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 15:28 +0000
              Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 16:30 +0100
      Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 09:23 +0100
        Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-22 11:08 +0000
        Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 12:54 +0000
  Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-21 17:39 -0800
    Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 13:00 +0000
      Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-22 05:31 -0800
  Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-22 11:04 +0000
    Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 12:53 +0000
      Re: A little puzzle. Paul N <gw7rib@aol.com> - 2022-11-22 05:01 -0800
        Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-22 05:48 -0800
          Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-22 15:31 +0100
      FFs [was Re: A little puzzle] Richard Harnden <richard.nospam@gmail.com> - 2022-11-22 16:29 +0000
    Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-12-14 13:57 +0000
      Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-12-14 13:58 +0000
      Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-12-14 16:22 +0000
  Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-22 05:24 -0800
    Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-22 15:23 +0000
      Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-23 08:04 -0800
        Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-24 00:06 +0000
          Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-24 04:06 +0000
            Re: A little puzzle. David Brown <david.brown@hesbynett.no> - 2022-11-24 09:29 +0100
              Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-24 13:23 +0000
            Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-24 13:14 +0000
              Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-24 14:00 +0000
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-24 14:59 +0000
                Re: A little puzzle. Richard Harnden <richard.nospam@gmail.com> - 2022-11-24 19:00 +0000
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-24 20:36 +0000
              Re: A little puzzle. Andreas <nobody@me.com> - 2022-11-27 00:38 +0100
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-27 00:11 +0000
          Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-24 14:51 -0800
            Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-25 09:30 +0100
              Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-25 01:16 -0800
                Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-25 11:11 +0100
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-25 06:26 -0800
                Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-25 15:59 +0100
            Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-26 16:25 +0000
              Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-26 19:36 +0100
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-27 02:03 +0000
                Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-27 11:02 +0100
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-01 04:30 -0800
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-12-02 00:22 +0000
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-02 22:30 -0800
                Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-12-03 02:43 -0800
              Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-27 18:38 -0800
  Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-27 02:27 -0800
    Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-27 19:23 -0800
      Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-27 22:59 -0800
        Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-27 23:03 -0800
        Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-28 07:22 -0800
          Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-28 10:20 -0800
            Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-29 04:29 -0800
              Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-29 04:50 -0800
                Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-29 14:47 +0000
                Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-29 17:23 +0000
                Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-29 09:50 -0800
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-30 01:39 -0800
                Re: A little puzzle. Richard Heathfield <rjh@cpax.org.uk> - 2022-11-30 11:10 +0000
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-30 02:24 -0800
                Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-30 06:28 -0800
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-01 06:55 -0800
                Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-12-02 01:54 -0800
  Re: A little puzzle. Richard Harnden <richard.nospam@gmail.com> - 2022-11-28 11:20 +0000
    Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-28 07:30 -0800
      Re: A little puzzle. Richard Harnden <richard.nospam@gmail.com> - 2022-11-28 17:15 +0000
        Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-29 04:03 -0800
          Re: A little puzzle. Richard Harnden <richard.nospam@gmail.com> - 2022-11-29 15:03 +0000
            Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-29 16:13 +0100
              Re: A little puzzle. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-11-29 17:37 +0000
                Re: A little puzzle. "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2022-11-29 19:02 +0100
                Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-29 10:10 -0800
            Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-11-30 03:32 -0800
              Re: A little puzzle. Julio Di Egidio <julio@diegidio.name> - 2022-11-30 06:36 -0800
              Re: A little puzzle. Richard Harnden <richard.nospam@gmail.com> - 2022-11-30 15:21 +0000
                Re: A little puzzle. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2022-12-01 06:51 -0800

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