The missing $1
Three people rent a room at $30. They pay $10 each and go up to the room. The owner realized he charged too much and it was only supposed to be $25. He sends the bell hop up with the $5. Each of the people keeps $1 and they give the bellhop $2 as they can't share it. So now each person has paid $9 for the room (total $27) and the bell hop has $2... where is the other $1?
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1 solution
The $1.00 isn't "missing" — it is an error to try to add the $27 and the $2. The $2 is the difference of $5 and $3 — it is not the true change in this transaction but is "change of change".
The people paid $30. They were given $5 back as change, but $2 of that change gets returned back to the owner as "change of change". In the end, the people have paid $27 total, and the owner receives $30 − $5 + $2 = $27, so it all matches.
Look at it this way: while the bell hop is going down the stairs, the owner has in his possession $25.00, each of the three people has $1.00 (x 3 = $3.00) and the bell hop has $2.00. $2 + $3 + $25 = $30.
Then when the bell hop returns the $2 to the owner, the owner has $27 and the three people have $3 in total.
Or look at it this way: What they get returned back are the dollars number 26, 27 and 28, and what they return the bell hop are #29 and #30.
Yet another way to think about the answer to this riddle is to just pretend that the bellhop refunded $3 to the people (rather than giving them $5 and receiving $2 back). If the lawyers get $3 back and each takes $1, then they spent exactly $27 dollars.
Hope it's clear..