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Math Help - Help needed for school puzzle

  1. #1
    Crossfire
    Guest

    Unhappy Help needed for school puzzle

    Here's the problem:
    "the answers below are correct even though the mutiplications are weird. What is the last answer?"

    12 23 34 45
    x34 x45 x56 x67
    ---- ----- ----- ----
    1013 2003 2663 ??


    Can ypu help me out?
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    745
    Hello, Crossfire!

    The answers below are correct even though the mutiplications are weird.
    What is the last answer?
    Code:
      12     23     34     45
    x 34   x 45   x 56   x 67
    ----   ----   ----   ----
    1013   2003   2663   ????
    Answer: . 3763

    The first multiplication is in base-5: . 12_5 \times 34_5\:=\:1013_5

    The second is in base- 6: . 23_6 \times 45_6\:=\:2003_6

    The third is in base-7: . 34_7 \times 56_7\:=\:2663_7

    The fourth is in base-8: . 45_8 \times 67_8\:=\:3763_8

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  3. #3
    Crossfire
    Guest

    Thanks

    Thanks for the help, but how did you know that it was in a different base?
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  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
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    Thanks
    745
    Hello, Crossfire!

    How did you know that it was in a different base?
    The sets of consecutive numbers got me thinking . . .
    . . 12 x 34, 23 x 45, 34 x 56, 45 x 67

    More important, I could see that the products were "too big".
    . . How can 12 x 34 produce a four-digit number?
    . . I knew that this happens when the number base is less than 10.

    The first multiplication had the digits 0, 1, 2, 3, 4.
    So I suspected a base-5 problem.
    I could have been wrong, but it worked out.

    The next had a 5, so it couldn't be base-5.
    I guessed that it might be base-6 . . . and I was right.

    So there was some luck involved, too . . .

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