Three poor farmers visit the big city for the first time. In the town, they visit a cheap hotel. The hotel owner is farmer-friendly: he has a room for 3 persons which costs only 30 dollars.

So, the farmers agree to pay $10 each. They pay and go to their room.

But then, the hotel owner realises that he has forgotten his super discount. The farmers only had to pay $25. So, he calls the bell-boy and tells him to give the farmers their $5 back.

But the bell-boy thinks: "You can't split 5 by 3 well. If I give them their $5, they'll probably have a fight." So he keeps $2 for himself and gives the other $3 to the farmers.

Now, the farmers each paid $9, that's $27 in total, and the bell boy kept $2. But together, that's $29!

What happened to the missing dollar?

I love this problem, and even though I've seen it before it STILL took me about 3 minutes to come up with the solution.

The problem with this problem =0) is that the logic of the question is incorrect.

The three farmers did pay $27, or 9 apiece, and the bellboy did keep $2. But the error is the assumption that these two values should be totaled. What we have to remember is that the bellboy didn't take the $2 from the manager, but rather from the men! The men paid $27, but the rate was only $25, which is where the bellboy gets his $2. $25 + $2 = $27, which is what was paid.

Now, on a separate note, do you think the farmers tipped the bellboy? I hope they stole the towles or something for that extra two bucks! =0)

Posted by Jim C on 2003-07-11 05:53:26