Posers and Puzzles

Posers and Puzzles

  1. Joined
    11 Nov '05
    Moves
    43938
    09 Jul '10 18:291 edit
    I found this interesting problem in New Scientist : http://www.newscientist.com/article/mg20727670.800-enigma-number-1602.html
    Solve it and be £15 richer.
    Note: I don't have the solution.

    - - - - - - - - - - - - - - - - - - - -

    Miscount
    I have assigned a whole number to each letter of the alphabet. These numbers are not necessarily different and they include negatives and zero. With these numbers I found that
    O+N+E = 1
    T+W+O = 2
    T+H+R+E+E = 3
    and so on all the way up to
    T+W+E+N+T+Y+N+I+N+E = 29.

    Unfortunately, I now find that I made one slip in my additions. Just one of my 29 equations was wrong.

    Which equation is wrong?
    What should the sum of the letters equal in that case?

    WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 4 August. The Editor's decision is final. Please send entries to Enigma 1602, New Scientist, Lacon House, 84 Theobald's Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
  2. ALG
    Joined
    16 Dec '07
    Moves
    6190
    09 Jul '10 21:43
    Originally posted by FabianFnas
    I found this interesting problem in New Scientist : http://www.newscientist.com/article/mg20727670.800-enigma-number-1602.html
    Solve it and be £15 richer.
    Note: I don't have the solution.

    - - - - - - - - - - - - - - - - - - - -

    Miscount
    I have assigned a whole number to each letter of the alphabet. These numbers are not necessarily different and ...[text shortened]... 's Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
    What if twenty is wrong?
    If twenty is wrong, then:
    - all other are correct
    - t+w+e+n+t+y is not 20
    o+n+e = 1 and t+w+e+n+t+y+o+n+e = 21
    the difference is t+w+e+n+t+y = 20
    So, twenty must be correct, and so are 1 - 9 and 21 - 29 (if two is wrong, twentytwo must also be wrong).
    For the same reason, 14, 16, 17, and 19 are correct.
    Only 10, 11, 12, 13, 15, and 18 can be wrong.

    What if 13 is wrong? Then:
    - all other are correct
    - t+h+i+r+t+e+e+n is not 13

    s+e+v+e+n+t+e+e+n = 17
    s+e+v+e+n = 7
    This makes, that t+e+e+n = 10 = t+e+n
    t + 2e + n = t+e+n
    2e = e
    e = 0

    e+i+g+h+t+e+e+n = 18
    e+i+g+h+t = 8
    This makes, that e+e+n = 10
    e = 0 --> 0+0+n = 10 --> n = 10

    e+e+n = 10 = t+e+e+n
    t = 0

    n+i+n+e = 9
    10 + i + 10 + 0 = 9
    i = -11

    t+h+r+e+e = 3
    0 + h + r + 0 + 0 = 3
    h + r = 3

    t+h+i+r+t+e+e+n is not 13
    0+ (h+r) -11 + 0 + 0 + 0 + 10 is not 13
    3 - 11 + 10 = 2 is not 13
    My presumption that 13 is wrong, is true.
  3. Joined
    11 Nov '05
    Moves
    43938
    09 Jul '10 21:55
    Originally posted by Thomaster
    What if twenty is wrong?
    If twenty is wrong, then:
    - all other are correct
    - t+w+e+n+t+y is not 20
    o+n+e = 1 and t+w+e+n+t+y+o+n+e = 21
    the difference is t+w+e+n+t+y = 20
    So, twenty must be correct, and so are 1 - 9 and 21 - 29 (if two is wrong, twentytwo must also be wrong).
    For the same reason, 14, 16, 17, and 19 are correct.
    Only 10, 11, 12, 13 ...[text shortened]... + 0 + 0 + 0 + 10 is not 13
    3 - 11 + 10 = 2 is not 13
    My presumption that 13 is wrong, is true.
    If you're correct in this, then mail the solution and the £15 is yours! 🙂
  4. ALG
    Joined
    16 Dec '07
    Moves
    6190
    09 Jul '10 23:00
    So my spelling is correct? It took a while to notice, that 18 is eighteen instead of eightteen. Should it be 'eight-een' or 'eigh-teen'?
  5. Joined
    24 Jan '09
    Moves
    5514
    10 Jul '10 02:33
    this is really cool puzzle
  6. Standard memberAgerg
    The 'edit'or
    converging to it
    Joined
    21 Aug '06
    Moves
    11458
    10 Jul '10 19:225 edits
    Originally posted by Thomaster
    What if twenty is wrong?
    If twenty is wrong, then:
    - all other are correct
    - t+w+e+n+t+y is not 20
    o+n+e = 1 and t+w+e+n+t+y+o+n+e = 21
    the difference is t+w+e+n+t+y = 20
    So, twenty must be correct, and so are 1 - 9 and 21 - 29 (if two is wrong, twentytwo must also be wrong).
    For the same reason, 14, 16, 17, and 19 are correct.
    Only 10, 11, 12, 13 ...[text shortened]... + 0 + 0 + 0 + 10 is not 13
    3 - 11 + 10 = 2 is not 13
    My presumption that 13 is wrong, is true.
    nevermind...thought you were *assuming* 13 false! It *is* false as you have indeed shown:]
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