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Three Men Rent a Hotel Room - A Semantic Fallacy
By Cynthia Kirkeby
Feb 22, 2007, 10:27

An employee of mine has posed this question to me and I can not come up with an answer.

    Three men rent a hotel room. Each pays $10 for a total of $30 spent on the room. The next day the hotel owner tells the three men that they over paid for the room as it only costs $25. The three men tell the owner to give them each a dollar back and he can keep two dollars.

    If you do the math, each man paid $9 a piece for the room for a total of $27. The owner kept $2 which brings the total to $29.

    The question is where did the other dollar go?

This question is driving me nuts. Can you help?

CTB


This actually isn’t as much a math problem, as a logic and semantics problem. It took me a few minutes to spot the logical fallacy in this problem. I knew it was there, but it was difficult to spot nonetheless.

This is a semantic fallacy. The premise is false, which you can see when you work the equation backwards. The men DID NOT pay $9.00 each for a total of $27.00 for the room. They each essentially paid $8.333 for the room for a total of $25.00. Then add back in the tip of $2.00 they gave to the hotel owner, equaling $27.00. Then add back the refund each man got back ($1.00 per man). This brings you back to your correct beginning total of $30.00.

Wording things in misleading ways is what allows swindlers to make a living. By wording it the way they have in the problem, you actually add in the $2.00 to the owner twice, and you don’t add in the $3.00 rebate to the men at all, which leaves you short $1.00.

Cynthia Kirkeby
ASK ClassBrain



Tony D has written it up another way... As you will see, we're essentially saying the same thing. The assumption in the original premise of $9 per man is incorrect. I worked the problem backwards and he works the problem forwards: "I read this riddle and realized, like you, that this seemingly mathematical impossibility is more a matter of semantics and deception than it is a mystery. The solution is so easy if you focus on the facts. The confusion begins with the explanation that the men…”paid $9.00 a piece…”. The $9 is not a fact; they didn’t pay $9 a piece; they paid $10 a piece. The math should start from the $10 not the $9. The solution thereafter is simple: Therefore: $10 x 3 = $30 $30 - $2 (amt owner kept) = $28 $28 - $3 (refund to renters) = $25 cost for the room" Once again, the math is simple if you ignore the misleading information set up in the puzzle. Keep your wits about you and watch out for semantic tricks.

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