3 ms·

Rewriting the question as if the room was supposed to be free also makes the bad math clear: > Three tourists stop at a hotel, and the manager tells them that

Rewriting the question as if the room was supposed to be free also makes the bad math clear: > Three tourists stop at a hotel, and the manager tells them that a shared room will cost $30. Finding the price agreeable, they pony up $10 each and retire to the room. Later that afternoon, the manager, who is honest, realizes that the room was meant to be priced at $0. The manager orders the bellhop to return the excess $30 to their guests. The bellhop, who is not honest, takes $30 from the register and return only $1 to each tourist, pocketing the remaining $27. > Now, each of the three tourists has spent $9, for a total of $27. The bellhop has retained $27, which brings the total to $54. Where did the other dollar go?

neogodless 5y ago
When you word it that way, I get a bit angry when I read "which brings the total to."
- mister_tee 5y ago
  Yes, that phrase is definitely doing some work here :). The followup might be "the total of what?" +1 to sibling post on proper bookkeeping but we can also sum inflow/outflow for each of the entities. There isn't a node where it makes sense to add +$27 and +$2. The customers collectively are at -10*3 + 1*3 = -$27. The hotel is at 10*3 - 5 = $25 The bellhop is at 5 - 1*3 = $2 And those sum to zero for the system; no money was created or destroyed. Or, thinking in terms of physical bills, the bellhop's two dollars are a subset of the 27 the customers paid out and adding them is double-counting. The real math behind the problem is just 27 = 25 + 2.