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missing dollar riddle

12/01/2007 4:55 AM

I heard this riddle, and it really has bothered me. I am sure that most people could see quite clearly the simple answer. Three people check into a hotel, they are going to share the room. The clerk charges them $30, and so each of the people put a 10 dollar bill on the counter. The clerk hands them the key, and the people go up to the room. Later on, the manager arrives at the clerks desk an tells the clerk about the special prices for the rooms and instead of $30 per room, the cost is only $25 per room. He hands the clerk $5 and tells the clerk to go up to the three peoples room and give them the $5. On the way to the room, the clerk decides that it will be much easier to give the three people $3, splitting the $5 between the three would be rather complicated. So he puts $2 in his pocket. After he hands each of the three people $1, that brings the total spent by each of the three people to $9 each. Now, since the three people have spent $9 each, making the total $27, and the $2 the clerk put in his pocket brings the grand total of $29. But we originally started with 3 ten dollar bills. Some people will tell me that its easy, the hotel took $25, then the $3, and the $2 makes a total of $30. Ok I see that, but what really bugs me is the fact that the three people have spent $9 each, and 3 times $9 is $27 plus the $2 in the clerks pocket makes $29.

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#1

Re: missing dollar riddle

12/01/2007 6:02 AM

The reasoning which is presented as part of the riddle, is false reasoning.

Cost to the 3 occupants was $10 x 3 = $30

Repaid to them was $5 (3 x$1.666666666666666) less $2 (3 x $0.666666666666666 kept by the clerk) = $3 ($1 each)

While the 3 people have each spent not the $9 as stated in the riddle.

The 3 people have thus spent each $9 + 1/3rd of the $5 (remember the $2 in the clerk's pocket - that $2 cost is split from the 3 guests)

The problem occurs in the riddle,when the sums are done incorrectly, to fool the hearer....

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#2

Re: missing dollar riddle

12/01/2007 8:43 AM

You are adding the $2 instead you should be subtracting it.

3 X 9 = 27 - 2 = 25 which is the cost of the room.

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#3

Re: missing dollar riddle

12/02/2007 2:11 AM

Although Sparky gave a correct and thorough response, you can sum it all up by saying that:

The $2 that the "riddle teller" added to the $27, is part of the $27 already...

Just add the $3 to the $27 to get a total of $30...

* They've spent $9 each, of which $2 the clerk has, and the $25 for the room = $27

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#4
In reply to #3

Re: missing dollar riddle

12/02/2007 2:51 AM

$25 for room

$2 is tip to clerk

Total $27 (each spent $9).

Now where is my dollar share for solving this riddle?

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#8
In reply to #4

Re: missing dollar riddle

12/03/2007 2:09 AM

You believe I should give you a dollar for repeating what I had already written in the previous post?

Besides, you wrote:

"$2 is tip to clerk"

The clerk stole the money, it wasn't given as a tip.

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#5

Re: missing dollar riddle

12/02/2007 3:02 AM

It is true that the 3 spent $9 each ($10 - $1). This total of $27 was shared by the hotel of $25 ($30 -$5) and the clerk who kept $2 totalling the $27 paid by the three.

It is clearer if one splits the $5 refund into 2 stages.

Stage 1 Hotel $30 - $2 kept by clerk leaving $28 before refunding guests.

Stage 2 Hotel $28 -$3 refund to guests.

So the $27 paid by guests goes to hotel $25 and clerk $2.

OK?

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#6

Re: missing dollar riddle

12/02/2007 8:48 AM

A Perfect Example of how figures don't lie, but liars figure!

Sounds like the cleck was a used car dealer previously.

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#11
In reply to #6

Re: missing dollar riddle

12/03/2007 4:24 PM

He prefers the term "pre-owned" to "used".

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#7

Re: missing dollar riddle

12/02/2007 6:58 PM

It actually cost them 27.00 since the clerk didn't give them back 2.00. (25.00 room cost+2.00 clerk stole) The 27.00 plus 3.00 (refund) is 30.00.

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#9

Re: missing dollar riddle

12/03/2007 7:56 AM

The way to see the puzzle and no longer go back and wonder is.

draw out 30 individual marks in groups of five in 3 rows 2 coloums then draw 1 circle that includes 1 at the end on the top row and 2 at the end of each of the other 2 rows. put an x on top of the 2nd to the end on row 2 and 3 (this represents the 2 dollars embezelled by the clerk.)

Each row represents one of the people, notice the false assumption that all three end up with equal amounts. It's the one extra on the top row above the 2 x'd out ones that is un-accounted for in the riddle's assumption.

1 1 1 1 1 1 1 1 1 (1)

1 1 1 1 1 1 1 1( X 1)

1 1 1 1 1 1 1 1( X 1)

Hotel ended up Keeping 25.00 on left. Clerk got 2.00 shown by x's.

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#10

Re: missing dollar riddle

12/03/2007 11:23 AM

I first heard this riddle when I was in Advance Electronics school (1982-83), I know there are a lot of ways to explain what actually transpired in a mathematical way, but it much more fun to keep people wondering.

The simple truth is that it is just a freak of math that does not work out when you add, subtract, multiply and divide.

I have much fun with this riddle over the years and some of my kid's teachers are still scratching their heads. LOL

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