I really like this one. Kudos to blaaf
for a good puzzler
, but for the longest time, I simply could not account for the final sentence:
So, the three businessmen each payed(sp) $9 (the $10 minus the $1 refund) for the room, a total of $27. The bellhop has the remaining extra $2 in his pocket. That adds up to $29.
While his solution gave an alternate way of looking at things, it did not give a reason as to why that last sentence was misleading. After a long period of deliberation, I came to the following conclusion:
In the beginning, the businessman paid $30. All the money in circulation (a total of $30) originally came from the businessmen and was held in the hotel's possession. After the $3 rebate, $25 was in the hotel's possession, $2 went to the bellhop, and the other $3 was held in the businessmen's possession. Therefore, the phrase "Each business man paid $9 for a total of $27" is true ($25 + $2).
The point of error in the aforementioned sentence is adding the bellhop's money to the money paid by the businessmen. Where did the bellhop's money come from? It came from the businessmen's originally paid money! The $2 didn't appear from nowhere, now did it? The $2 is part of, and not in addition to, the $27 that the businessmen paid. Add the $3 (rebated money that the businessmen now possess) and now you come to the $30 originally in circulation.