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Heymatt:

My brother-in-law used to tell me this riddle all the time, but he passed away a few years ago and now none of my family can remember the answer, if ever there was one: “Three guys check into a hotel and each pay \$10 to share a \$30 room. Later, the clerk realizes the room was supposed to be \$25 and he takes five \$1 bills to the guys in the room. Each guy takes \$1 back and they give the clerk a \$2 tip. Since the guys got one dollar back, they each paid \$9 for the room. 3x\$9=\$27. Add the \$2 tip and you have \$29. Where did the other dollar go?”

— Ken, Cardiff

More than a riddle, this is a classic example of deceit via misdirection and logical fallacy. The exercise describes a bogus sort of “cash reconciliation” that sets up some false premises and makes you assume some things that aren’t true. “The guys each paid \$9” is the biggest lie. Just look at it this way, if they each paid nine dollars for the room, they would have paid \$27 for a \$25 hotel room! We know the room was \$25, because the guests shelled out \$30 at the beginning and then \$5 comes back. It’s easy to lose track of the real monies when following a series of dubious facts and misdirected assumptions. The classic change-raising con works in much the same way. A grifter can convince a hapless store clerk to miscount cash by setting up bogus math that works out in the con-man’s favor.

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#### Javajoe25Feb. 8, 2013 @ 3:39 p.m.

Here's one for you Matt;

Pick a number from one to ten. Don't tell me which number you picked.

Now, multiply the number by 9. I know--you should have picked a lower number. But do it; you can do it; multiply the number by 9.

Now you have a new number composed of two digits. Add those digits to get a new number. Good. Now you have a new number.

Now take five from that number (stay with me; I know you can do it!), which gives you a new number again.

Okay. Now find the letter in the alphabet that corresponds with your new number. You know--1 is A, 2 is B...etc.. Which letter corresponds with your number?

Very good. Now you have a letter. Pick a country that starts with that letter. Come on--you can do it, I know you can do it. Think! Think! A country that starts with that letter.

Excellent! Now, take the second letter in that country's name and pick an animal that starts with that letter.

Show of hands--how many of you have an elephant in Denmark? Eagle in Denmark? No? Go back and do the math again. Or, tell me what you came up with.

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#### Matthew_AliceFeb. 8, 2013 @ 9:49 p.m.

Isn't this the actual riddle that Bilbo Baggins uses to stump Gollum in the book?

And, yes, I had a Danish elephant in mind. Well played.

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#### Matthew_AliceFeb. 8, 2013 @ 9:47 p.m.

I got an email from a sharp reader with an alternative, much simpler explanation that relies on principles of human nature:

"People tend to get scared off from actually figuring this out because many have believed most of their lives that they can't do math, even if it's simple addition and subtraction." -- Mark

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#### Matthew_AliceFeb. 8, 2013 @ 9:58 p.m.

Nik from PQ provides yet another clever way to suss out the truth on this:

"Try it with more extreme numbers: three guys check into a hotel room and each pay \$33 to share a \$99 room. Later, the clerk realizes the room was supposed to be \$3 and he takes 96 \$1 bills to the guys in the room. Each guy takes \$1 back and they give the clerk a \$93 tip. Since the guys got one dollar back, they each paid \$32 for the room. 3x\$32=\$96. Add the \$93 tip and you have \$189. Where did all the extra money come from?"

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