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Where is the other dollar?

August 18, 2009
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A friend sends along the following puzzle:

Three salesmen decided to share a $30 hotel room for one night and split the cost evenly between them.

After they checked in, the hotel manager noticed that they should have been charged only $25 for the room. So, he gave the porter five one-dollar bills and said to return the money to the three men.

As the porter was walking to the salesmen’s room, he wondered how he was going to split the five dollars evenly between the three salesmen. So, he put two dollars in his pocket and gave each of the three salesmen one dollar.

Now, if each of the salesmen paid $10 for their share of the room and were given one dollar back, then they each would have paid $9 for the room. Nine times three is twenty-seven, plus the two dollars the porter put in his own pocket is twenty-nine (9 x 3 = 27. 27 + 2 = $29)
Where is the other dollar?

h/t Barry.

Three salesmen decided to share a $30 hotel room for one night and split the cost evenly between them.
After they checked in, the hotel manager noticed that they should have been charged only $25 for the room. So, he gave the porter five one-dollar bills and said to return the money to the three men.
As the porter was walking to the salesmen’s room, he wondered how he was going to split the five dollars evenly between the three salesmen. So, he put two dollars in his pocket and gave each of the three salesmen one dollar.
Now, if each of the salesmen paid $10 for their share of the room and were given one dollar back, then they each would have paid $9 for the room. Nine times three is twenty-seven, plus the two dollars the porter put in his own pocket is twenty-nine (9 x 3 = 27. 27 + 2 = $29)
Where is the other dollar?
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2 Comments leave one →
  1. Kyle permalink
    August 19, 2009 9:04 pm

    “then they each would have paid $9 for the room.”

    Not correct… they each paid $9 for the room AND for the porters “tip”…
    ($9 x 3 = $27 = $25 + $2)

    “Nine times three is twenty-seven, plus the two dollars the porter put in his own pocket is twenty-nine (9 x 3 = 27. 27 + 2 = $29)”

    The two dollars to the porter is included in the twenty-seven, this counts the two dollars to the porter twice…

    Nice one! I like it!

  2. Flex727 permalink
    August 23, 2009 4:17 pm

    I think the simple way to look at it is that, in the problem, the $2 is added instead of subtracted and the result, by happy coincidence (or design), is close enough to the original $30 to make an interesting brain teaser.

    Or what Kyle said. 🙂

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