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Posers and Puzzles

Posers and Puzzles

  1. Standard member wolfgang59
    Infidel
    30 Dec '13 01:48
    1 = 5
    2 = 505
    3 = 5005
    4 = 50005
    5 =

    ?
  2. Subscriber coquette
    Already mated
    30 Dec '13 07:15
    Originally posted by wolfgang59
    1 = 5
    2 = 505
    3 = 5005
    4 = 50005
    5 =

    ?
    5 = 1

    as 1 = 5
  3. 02 Jan '14 16:59
    the digits of each number can be rearranged to give n other valid numbers (i.e. without leading zeros)

    e.g.
    505, 550
    5005,550,5050
  4. Standard member wolfgang59
    Infidel
    02 Jan '14 22:24
    Originally posted by coquette
    5 = 1

    as 1 = 5
    correct
  5. 03 Jan '14 22:33
    Originally posted by wolfgang59
    1 = 5
    2 = 505
    3 = 5005
    4 = 50005
    5 =

    ?
    but, it is ambiguous:


    1 = 5 which has 1 possible arrangement (5)
    2 = 505 which has exactly 2 possible arrangements (505, 550)
    3 = 5005 : 3 arrangements (5005, 5050, 5500)
    4 = 50005: 4 arrangements (50005, 50050, 50500, 55000)

    so the fomula could be:
    for any number n, the lowest number, made of only the digits 0 and 5, which can be rearranged into n distinct legal numbers.

    so
    5 = 500005
  6. 03 Jan '14 23:21
    Your solution is not unique. 55000, 50500, 50050 also fits your requirements.
  7. 04 Jan '14 10:09 / 1 edit
    Originally posted by Sebastian Yap
    Your solution is not unique. 55000, 50500, 50050 also fits your requirements.
    As I said:

    for any number n, the lowest number, made of only the digits 0 and 5, which can be rearranged into n distinct legal numbers, i.e. 50005. This also fits the given numbers.
  8. Standard member talzamir
    Art, not a Toil
    18 Jan '14 23:28
    f(n) = 5 + 5 x 10^n would be good for most cases but not f(1).. oh well.

    "lowest POSITIVE number.." and Tiger's wording is even more flawless, eliminating negative numbers and 1 = 0.
  9. 20 Jan '14 09:00
    Originally posted by talzamir
    f(n) = 5 + 5 x 10^n would be good for most cases but not f(1).. oh well.

    "lowest POSITIVE number.." and Tiger's wording is even more flawless, eliminating negative numbers and 1 = 0.
    Good point talz!