Re: modular arithmetic

From: Richard S. Holmes (rsholmes_at_MailBox.Syr.Edu)
Date: Thu Sep 27 2001 - 09:02:28 PDT

I suppose it makes no difference that I'm the rule's author, but I'll
mention that anyway, before saying:

(1) "Modulo 5" was a mistake; I meant "modulo 6".  I'm surprised I
    didn't lose style points for such a blunder.

(2) Not being a mathematician, my original intent was that one should
    take the number of letters in a word, divide by six, and take the
    remainder, yielding a number in the range 0 to 5 inclusive.  With
    the above error, my *intent* would have been to allow the range 0
    to 4 inclusive.

(3) However, intent, schmintent!  And without throwing around scary
    phrases like "equivalence classes", I think Anton has a perfectly
    good argument, that the sentence in question can be interpreted as
    requiring only that the number on the die and the number of
    letters in the word be equal (or congruent) modulo 5, so that a
    word of 5 letters can be used to generate either a 0 or a 5.

I therefore would support a reversal on 169:7, even though I too
originally believed it violated my rule.

- Rich Holmes
  Syracuse, NY

Rule Date: 2001-09-27 16:02:47 GMT

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