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  • Re: (5* 142857 =714285) -- Rotate Tail to Head is x5 (factor of 5)

    From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Sun Jun 14 08:04:43 2026
    From Newsgroup: rec.puzzles

    On Thu, 11 Jun 2026 08:44:30 +0000, HenHanna wrote:

    Other factors?

    Any single digit other than 0 and 1.

    In her book 'Mathematical Excursions' (p.60) Helen Abbot Merrill points
    out that the sequence of digits which provide a solution to these problems
    are the same as the repeating period in the fraction given by x^2/(10x -
    1), where x is the digit changing places.

    Would anyone like to explain why?
    --
    David Entwistle
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Sun Jun 14 08:19:03 2026
    From Newsgroup: rec.puzzles

    On Sun, 14 Jun 2026 08:04:43 -0000 (UTC), David Entwistle wrote:

    Any single digit other than 0 and 1.

    In her book 'Mathematical Excursions' (p.60) Helen Abbot Merrill points
    out that the sequence of digits which provide a solution to these
    problems are the same as the repeating period in the fraction given by x^2/(10x - 1), where x is the digit changing places.

    Having looked more closely at your post, I should have made it clear that Helen Abbot Merrill is describing the case where the digit moving and the multiplier are the same. That is somewhat different to what you have in
    your subject line.
    --
    David Entwistle
    --- Synchronet 3.22a-Linux NewsLink 1.2