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Posers and Puzzles

Posers and Puzzles

  1. Standard member wolfgang59
    Infidel
    25 Jun '15 23:12
    6 people talking at a party discover they all live on the same street.
    One says but my address is rather unique - my house number has 3 digits and the sum of those digits is equal to the product!

    In unison the other 5 say "So do mine!"

    How close are the nearest neighbours?
  2. 27 Jun '15 20:29
    The 6 people live at the following numbers: 123, 132, 213, 231, 312, 321. The closest pairs are (123,132) and (312,321), both differ by 9. I guess you could say the closest would be (123,132) assuming 1 is opposite 2, 3 is opposite 4, etc...
  3. Standard member wolfgang59
    Infidel
    27 Jun '15 20:36 / 1 edit
    Originally posted by Zuggy
    The 6 people live at the following numbers: 123, 132, 213, 231, 312, 321. The closest pairs are (123,132) and (312,321), both differ by 9. I guess you could say the closest would be (123,132) assuming 1 is opposite 2, 3 is opposite 4, etc...
    The pairs you quote are on opposite sides of the street so
    no way of determining closeness and in British English usage
    not "neighbours". The answer I was looking for was 213 & 231.
  4. Subscriber joe shmo On Vacation
    Strange Egg
    28 Jun '15 00:40
    Originally posted by wolfgang59
    The pairs you quote are on opposite sides of the street so
    no way of determining closeness and in British English usage
    not "neighbours". The answer I was looking for was 213 & 231.
    Is there a way to solve

    a + b + c = a*b*c

    To arrive definitively at those results?
  5. Subscriber Ponderable
    chemist
    02 Jul '15 15:06
    Originally posted by joe shmo
    Is there a way to solve

    a + b + c = a*b*c

    To arrive definitively at those results?
    one equation with three unknowns is not definitely defined.

    what you can do is to apply some logic on the digits:

    * no "0" involved since the product involving zero is zero, but 000 is not a valid three digit number.
    * not more than one digit may be 1 since 1*1*n=n but 1+1+n=n+2

    from the first two: no digit bigger than 3 since the smallest including 4 is 124 with 1+2+4=7 and 1*2*4=8, the products increase faster than the sums.

    so 123 and its permutations are left over 1+2+306 1+2*3=6, all valid solutions are:

    123 132 213 231 312 321 as given above.
  6. Standard member wolfgang59
    Infidel
    03 Jul '15 01:27
    Originally posted by Ponderable
    one equation with three unknowns is not definitely defined.

    Not true if we are dealing just with positive integers.
    eg What is the solution to A+B+C=3
  7. Standard member forkedknight
    Defend the Universe
    06 Jul '15 16:39
    Originally posted by wolfgang59
    Not true if we are dealing just with positive integers.
    eg What is the solution to A+B+C=3
    This may be true, but the problem at hand is dealing with non-negative integers, not positive ones
  8. 20 Jul '15 11:34 / 1 edit
    Originally posted by wolfgang59
    How close are the nearest neighbours?
    Not very close.

    I mean, they live on the same street but apparently don't know this.