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Posers and Puzzles

Posers and Puzzles

  1. 24 Apr '08 22:29
    A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

    Three guys walk into a hotel and get a room. The room is $30, so each guy coughs up $10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a $5 bill, and tells one of his employees to take it up to the room. On his way up there, the guy realizes that they can't possibly split $5 between three guys. He takes out his wallet, puts the $5 bill in it, and takes out three $1 bills. He keeps $2. Each guest gets $1. Now it's like they each paid $9 for the room. $9 x 3 guys = $27, $27+ $2 (the money the employee kept for himself) = $29.

    Where'd the missing dollar go?
  2. 24 Apr '08 22:32
    The $2 is included in the $27, so you shouldn't add it again. $25 with the hotel, $2 with the guy, and $3 with the other guys = $30.
  3. 24 Apr '08 23:03
    This particular problem is deceptive (and intentionally so) because it gives you a logic that has an inconsistent frame of reference.

    So let us examine the facts, then process into the account, shall we?

    To simplify things, the three men will be considered a single party, as there really isn't anything distinguishing one from the other.

    1) The Men pay the Manager $30.
    2) The Manager hands the Bellhop $5.
    3) The Bellhop hands the Men $3.

    Three transactions, now let us track where the $30 is

    Before step one, the Men have $30, and the Manager and Bellhop have $0 each.

    After payment, the Manager has $30, and the Bellhop and Men $0.

    After the Manager tasks the Bellhop, the Manager has $25 (NOT $27), the Bellhop $5, and the Men $0.

    After the Bellhop performs the incomplete refund, the Manager still has $25, the Bellhop $2, and the Men $3. Sum total is $30.

    So as the second poster has pointed out, the $27 paid includes both the Manager's revenue and the Bellhop's "fee", and the remaining $3 is back with the men.
  4. Standard member wolfgang59
    Infidel
    25 Apr '08 15:25
    Originally posted by golfer1
    A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

    Three guys walk into a hotel and get a room. The room is $30, so each guy coughs up $10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a $5 bill, and tells one ...[text shortened]... $27+ $2 (the money the employee kept for himself) = $29.

    Where'd the missing dollar go?
    Obviously the maid got it.
  5. 25 Apr '08 16:08
    Originally posted by wolfgang59
    Obviously the maid got it.
    The maid made a buck...
  6. 27 Apr '08 21:50
    Originally posted by golfer1
    A friend of mine told me this riddle, and I'm trying to figure out an explanation for why this happens. Here goes:

    Three guys walk into a hotel and get a room. The room is $30, so each guy coughs up $10. After they go up to their room, the manager realizes that he overcharged them for the room. He opens up the register, takes out a $5 bill, and tells one ...[text shortened]... $27+ $2 (the money the employee kept for himself) = $29.

    Where'd the missing dollar go?
    30-5=25 with manager

    5-3=2 with employee

    1+1+1=3 with each of three guys

    25+2+3=30


    Why did you think there would be 29$, I don't understand?
  7. 27 Apr '08 23:05
    Originally posted by UzumakiAi
    30-5=25 with manager

    5-3=2 with employee

    1+1+1=3 with each of three guys

    25+2+3=30


    Why did you think there would be 29$, I don't understand?
    The problem is intentionally worded with false, inconsistent logic.

    The person posing this intentionally counts the bellhop's $2 separately from the $27 the men paid (when it is actually a part of it), and intentionally ignores the $3 they got back.

    The problem is solved when the solver realizes this and frames the problem properly.
  8. 27 Apr '08 23:10
    Originally posted by geepamoogle
    The problem is intentionally worded with false, inconsistent logic.

    The person posing this intentionally counts the bellhop's $2 separately from the $27 the men paid (when it is actually a part of it), and intentionally ignores the $3 they got back.

    The problem is solved when the solver realizes this and frames the problem properly.
    Oh. Strange.