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Final Brain Teaser #23 ~ Forza1: Wanted Dead or Alive

Discussion in 'Other Off Topic Forum' started by PeterS, Jul 17, 2004.

  1. PeterS

    PeterS Three Time F1 World Champ
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    Forza1 saw his face on a poster nailed to a tree. As he approached, he saw "Wanted: Dead or Alive". Under his picture, it read "Reward: ___Dollars".

    There was a three digit figure on the poster. Forza1 drew his Colt and shot at the first number (In the hundreds column). He had just reduced the price on his head by five times!

    "Good Lord!" came the voice of NNO, who was sitting on the other side of the tree, pounding out a fresh Ferrari article. Forza1 blushed and shot again at another number (In the tens column). He had just reduced the price on his head by another five times!

    "Nice shooting!" said NNO, almost done with his article. "Thank you" said Forza1, who got on his horse and rode into the sunset.

    What was the initial reward offered on Forza1's head?
     
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  3. Turb0flat4

    Turb0flat4 Formula 3

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    $ 125

    Setting the last one a little too easy ? After your nine digit problem this is a doddle. :D

    Let the reward be 100A + 10B + C in dollars.

    We have that :

    100A + 10B + C = 5*(10B + C) ---(1)

    and

    10B + C = 5*C ---(2)

    From (2),

    10B = 4*C

    and for non trivial integer solution set 9 or less, we need B = 2, C = 5

    Putting that back into (1), we get A = 1, and the answer.
     
  4. PeterS

    PeterS Three Time F1 World Champ
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    Good job!
     
  5. Turb0flat4

    Turb0flat4 Formula 3

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    Just thought of a far more elegant way of doing it.

    The whole number is 5*5*(units digit). That means it's a multiple of 25. All multiples of 25 necessarily end with 5 or 0, which means the last digit has to be either of those.

    The last digit can't be zero, because that would give the trivial solution of $0, so the last digit has to be 5.

    Then the whole number has to be 5*5*5 = 125.
     

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