Ancient Chestnut #1 (Hotel)

[Ghost Post]

Even if this is already eaxplained elsewhere, I will add my explanation. First, of all there is no missing dollar. Only a misleading accounting strategy can result in a "missing dollar.

Let g, m, and b, stand for the relative amount of money held by the guests collectively, the manager, and the bellhop. That is, let g = 30, m = 0, and b = 0.

"Each gives the manager a ten"

Now, g = 0, m = 30, and b = 0.

"The manager gives the bellhop five dollars."

Now, g = 0, m = 25, and b = 5.

"The bellhop gives them a dollar each an keeps two."

Now, g = 3, m = 25, and b = 2.

At every stage, g + m + b = 30. There is no missing dollar. The ambiguous part is "Now each of the men paid $9.00 for the room, for a total of $27.00. The bellhop has $2.00. 27+2=29. What happened to the missing dollar?"

The point is that eah man PAID $9.00, which we can represent as -9. The manager has +27 and the bellhop has +2. The debt plus the income should always equal zero (or else dollars were created or destroyed). We see:

3(-9) + 25 + 2 = 0.

Therefore, contrary to what the Minotaur insinuates, money (like mass, energy, momentum, charge, etc.) is conserved.

The last two lines of the puzzle should read, "Now each of the men paid $9.00 for the room, for a total of $27.00. The bellhop has $2.00. The manager has $25. 25 + 2 = 27. There is no missing dollar."

Shortly, the manager remembers that the room was at a discount, on
account of it being haunted. So he tells his bellhop that the room was only
$25.00, gives the bellhop five dollars and tells him to give the men the refund.

The bellhop is slightly crooked and rationalizes, "Five doesn't divide well
among three, I'll save them some arguing and just give them a dollar each."
Which he does, and keeps the leftover two dollars for himself.

Now each of the men paid $9.00 for the room, for a total of $27.00. The
bellhop has $2.00. 27+2=29. What happened to the missing dollar?