This one drove me crazy for a while. Let's see how you do.
Three guys are driving cross country together, and stop in at a motel late one evening. The night manager tells them there's only one room left, and it costs $30. The guys are exhausted, so rather than drive on looking for a motel with separate rooms, they take the single and cough up $10 apiece.
The next morning the day manager looks at the books and sees that the guys were overcharged $5. He takes five dollar bills out of the cash register and gives them to the motel janitor to take to the three guys as a refund. On the way, the janitor pockets $2 for his troubles, and gives the three guys a dollar apiece.
After their refund the three guys only paid $9 each, or $27 total. But they gave the night manager $30, and the janitor only kept $2.
Where did the extra dollar go?
The answer is really simple, once you see it. You can read it, along with my attempt to explain it, below.
The short answer is that there is no "extra dollar." Another way of looking at it might be to say that the motel wound up with the "extra dollar," but that wouldn't be quite right.
You see, this little puzzle is really just an example of how slippery words can be. To make the problem a little less confusing, let's switch to numbers, instead.
There are two different ways of describing this story correctly.
- Three guys pay $30 for a room. The hotel gets $25 after the refund, the guys keep the $3 refund, and the janitor pockets $2.
Three guys pay $9 each for a room, for a total of $27. The hotel gets $25,and the janitor pockets $2.
No problem there, right? If you reduce these two versions of the story to numerical equations, you get the following:
27 = 25 + 2.
Still no problem. But the way the story is worded, you wind up confusing the two equations in your head. The story talks about the $30 the guys originally paid and the $27 they ended up paying after the discount, but those two numbers are from two different equations. The confusion arises from the suggestion that the two numbers 30 and 27 are somehow related, when they really aren't. And no matter how hard you try, you won't be able to use the $2 taken by the janitor (from either equation) to get 27 to equal 30 (see the figures in bold).