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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