A Straight Dope Classic from Cecil's Storehouse of Human Knowledge

# Riddle: The 3 guys, the bellhop, and the missing buck

June 21, 1991

Dear Cecil:

Recently I got into an argument over this riddle:

"Three sailors decided to share a motel room for \$30 a night or \$10 each. After they've checked in the manager feels guilty for charging so much, so he gives the bellhop \$5 to take to the sailors. The porter is mad at the sailors for not tipping him, so he keeps \$2 and gives each man \$1.

"Each sailor now has paid \$10 - \$1 = \$9. \$9 x 3 = \$27. Add the \$2 the bellhop kept and we have \$29. Where is the other dollar?"

Well?

Cecil replies:

I got this same question in the same mail from Sam B. of Austin, Texas. You guys part of some cult?

I don't see what the big mystery is. The sailors paid \$27. The motel got \$25, the bellhop \$2. Total paid: \$27. Total received: \$27. The books balance; no missing dollar.

Your problem is thinking that what the sailors PAID plus what the bellhop RECEIVED should equal \$30. It shouldn't. It's only happenstance that the total comes as close as it does.

Suppose the sailors had initially paid \$45 for their \$25 room — \$15 each. The manager feels guilty and gives the bellhop \$20 to give back to them. The bellhop keeps \$17 and gives the men \$1 each.

Each man has now paid \$14 — \$42 in all. The bellhop has \$17. \$42 + \$17 = \$59 — only now we're so far off the original \$45 that it doesn't occur to you to ask where the "missing" \$14 is.

Many riddles work by suggesting a relationship where there isn't one. Take the old schoolyard trick where someone "proves" you have 11 fingers. First he counts down the fingers on one hand: "10, 9, 8, 7, 6." Then he grabs your other hand and says, "plus 5 makes 11."

By the time you were in sixth grade I imagine you saw through that fraud; now you've seen through this one. Next week we'll work on Ross Perot.

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