# Missing Dollar?

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3 guys want to share a hotel room and the costs. The clerk charges them \$30 (\$10 apiece) and sends them up to their room so they can rest. Later he discovers that he's overcharged them for the room, the correct rate for that room is only \$25 per night. He sends the bell hop up to their room with their \$5 refund. On the way up to their room the bell hop is wondering how he's supposed to split \$5 between 3 different guys. In order to avoid the hassle he pockets \$2 of the \$5, leaving a \$3 refund to split between the 3 friends. He does this and leaves... everyone is happy right? Except for the mathematician... the 3 friends each paid \$9 apiece for the room (\$10 minus the \$1 refund) which makes a total cost of \$27 (\$9 times 3) for the room. \$27 plus the \$2 the bell hop kept only equals \$29 where'd the missing dollar go? In the mathematicians wallet, that's his cut for making you believe that numbers are perfect...

I once knew the solution, but now I've forgotten...
Can someone help me?
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Anne, I too have heard this puzzle and I too know its solution. But I couldn't remember!

I've been thinking for the past 10 min,. but to no avail. Let me continue..tic...tic...tic...
All I do remember is that it's the wrong question that's asked.
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I have got a closer-solution.

Let's solver it using bottom-up approach. Firstly, the room costs \$30 and then the boy keeps \$2. Hence, the room rent is \$28 and not \$27 as assumed.

Therefore 28 + 2 = 30 !!!!
That's not it...
I think the question is correct.

Let me think for a better solution.
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30 - 3 = 27
the 2 left (from the five) are for the bell boy, and not the three left from above...
It's a confusing one this, but there is no missing dollar.

The three men paid \$25 for the
motel room and the bellhop kept \$2, for a
total of \$27 (\$9 each man).
Another way of looking at it :

The facts in this riddle are clear: There is an initial \$30 charge. It should have been \$25, so \$5 must be returned and accounted for. \$3 is given to the 3 friends, \$2 is kept by the bellhop - there you have the \$5. The trick to this riddle is that the addition and subtraction are done at the wrong times to misdirect your thinking - and quite successfully for most. Each of the 3 friends did indeed pay \$9, not \$10, and as far as the friends are concerned, they paid \$27 for the night. But we know that the clerk will tell us that they were charged only \$25 and when you add the \$3 returned with the \$2 kept by the bellhop, you come up with \$30.
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