Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math related riddle

  1. Jun 3, 2004 #1
    Math related riddle!!!

    Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the missing $1?

    Good luck you'll need it!!!
  2. jcsd
  3. Jun 3, 2004 #2
    "Now each person paid $10 and got back $1. So they paid $9 each, totalling $27."

    The people paid BOTH the hotel room bill AND (unknowingly) the bellboy $27 total ($25 + $2). $25 charged for the hotel room; $2 kept by bellboy

    What isn't accounted for yet is the $3 the people got back.

    "The bellboy has $2, totalling $29."

    $2 was already accounted for in the $27. Why add it again?

    "Where is the missing $1?"

    Nothing is missing. Complete the accounting with $27 (hotel AND bellboy) + $3 (change from $30) = $30 (money originally paid by the people)



    If you like it better:

    per person: ($8+$1/3) share of room charge + ($2/3) secret bellboy tax + ($1) refunded = $10 originally paid amount
    Last edited: Jun 3, 2004
  4. Jun 3, 2004 #3
    Yup you're correct!
  5. Jun 4, 2004 #4
    It is an old puzzle. I haven't heard it for a long time. It illustrates two good points:

    1. People are reluctant to deal with fractions, so they are easily distracted by exact integer amounts ($30 paid, $3 back).

    2. People are easily overcharged when hidden surcharges are buried inside a payment and they are induced into paying them again.

    Best of Luck!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook