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Posers and Puzzles

Posers and Puzzles

  1. 26 Mar '03 03:03 / 2 edits
    A set of numbers as follows in 5 colums:

    1______2______3______4______5
    9______8______7______6______-
    -______10_____11_____12_____13
    17____16_____15_____14______-
    -______18_____19_____20_____21

    and so on (ignore the - and _ I've included them to make formatting better).

    If I asked what column is 18 in, you would say column 2.
    The problem is as follows.

    Derive a formula which will provide the column any specific number lies in given that the above pattern continues to infinity. i.e. the number x lies in column y.

    Good luck.
  2. Donation Acolyte
    Now With Added BA
    26 Mar '03 17:39
    Originally posted by Lazaraus
    A set of numbers as follows in 5 colums:

    1______2______3______4______5
    9______8______7______6______-
    -______10_____11_____12_____13
    17____16_____15_____14______-
    -______18_____19_____20_____21

    and so on (ignore the - and _ I've included them to make formatting better).

    If I asked what column is 18 in, you would say column 2.
    The problem is as ...[text shortened]... that the above pattern continues to infinity. i.e. the number x lies in column y.

    Good luck.
    How about this:

    y = min(f(x-1)+1,f(-x)+2)

    where f(a) = b : 0<=b<=7 and b=a (mod 8)
  3. 26 Mar '03 22:59
    Originally posted by Acolyte
    How about this:

    y = min(f(x-1)+1,f(-x)+2)

    where f(a) = b : 0<=b<=7 and b=a (mod 8)
    That seems to work - well done.
    How long did it take you?
  4. Donation Acolyte
    Now With Added BA
    29 Mar '03 09:00
    Originally posted by Lazaraus
    That seems to work - well done.
    How long did it take you?
    A few minutes. I noticed it was doing something modulo 8, so I wrote out a table and noticed I could get what I wanted as the minimum of two things.