From: david.brown@hesbynett.no   
      
   On 21/11/2022 22:21, Ben Bacarisse wrote:   
   > David Brown  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?   
      
   >>   
   >> 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".  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.   
      
   >   
   > 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...   
      
   --- SoupGate-Win32 v1.05   
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