Oct 14, 2010

Where Did The $1 Go?

Okay, this mathematical anomaly has drive me crazy for a while, before I got the answer when browsed the web. Can you solve it before check the answer?

Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room.

A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in.

The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day!

Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent. Where did the other dollar go?

The Answer

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.

Note: Some people still won't get it after reading the answer, don't blame me though. For conclusion, it's just a matter of perception.

Fun or Not:


Bingo.com said...

I feel so fool lol!

Ken @ Thermal Mugs said...

I like that one - I initially thought it was due to rounding the amount, but that didn't work as they didn't pay a fraction. Going to pass this one to a friend who's a Math teacher - she can probably use it as an end of period puzzle or something of that sort!

The Invisible Man said...

So the rooms cost $8.333333 each did they?

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