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Posers and Puzzles

Posers and Puzzles

  1. Standard member wolfgang59
    Infidel
    25 Aug '15 22:22
    So little action on this forum I've contrived this little puzzle.

    Five couples live on the same street, they are amazed to discover that the reciprocals of their house numbers when summed is equal to 1.

    Furthermore when one of the couples gets divorced and they sell their property to buy two houses the reciprocals of all 6 houses sums to 1.

    At what number did the divorced couple live at?

    (Probably multiple solutions ... I have the easy one!)



  2. Subscriber Ponderableonline
    chemist
    26 Aug '15 12:56
    I wrote a lengthy bit on how to obtain the numbers, but I leave you with the solution only:

    5 houses: 2,3,12,18,36

    6 houses: 2,6,9,12,18,36
  3. Subscriber Ponderableonline
    chemist
    26 Aug '15 14:36
    Originally posted by Ponderable
    I wrote a lengthy bit on how to obtain the numbers, but I leave you with the solution only:

    5 houses: 2,3,12,18,36

    6 houses: 2,6,9,12,18,36
    The former post was wrong...

    I think there are a lot of solutions, lets try for a few:

    5 pairs: 2,4,9,12,18
    6 pairs: 3,4,6,9,12,18 (splitting the 1/2 into 1/3 + 1/6)

    5 pairs: 3,4,5,6,20
    6 pairs: 3,4,5,9,18,20 (splitting the 1/6 into 1/9+1/18)

    5 pairs: 2,4,9,12,18
    6 pairs: 2,5,9,12,18,20 (splitting the 1/4 into 1/5 and 1/20)

    5 pairs: 2,4,9,12,18
    6 pairs: 3,4,6,9,12,18

    5 pairs: 2,4,9,12,18
    6 pairs: 2,4,9,16,18,48

    ...and so on
  4. Standard member wolfgang59
    Infidel
    26 Aug '15 23:57
    Originally posted by Ponderable

    I think there are a lot of solutions, lets try for a few:

    5 pairs: 2,4,9,12,18
    6 pairs: 3,4,6,9,12,18 (splitting the 1/2 into 1/3 + 1/6)

    ...and so on
    Good enough.