Maths Riddle~

[AltumAngel]

Three friends check into a hotel 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 three by $5. He asks the bellboy to return $5 to the three friends who had just checked in.

The bellboy 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?

[chemist]

We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent.

Well, the answer to this riddle lies in the sentence above, which should read: "We know the bellhop pocketed $2 and subtracting that from the $27, you get $25 (30-5), which is what the clerk got to keep."

To put it another way, we could examine what was actually spent and kept during the two stages in this scenario.

Stage 1: Spent: $30 ($10 each) by the friends. Kept: $30 by the clerk.

Stage 2: Spent: $27 ($9 each) by the friends. Kept: $2 by the bellboy, $25 (27 - 2) by the clerk.

Or, alternatively:

Stage 2: Spent: $27 ($9 each) by the friends, -$2 by the bellboy (he gained $2 by theft). Kept: $25 (27 + -2) by the clerk.

So, the other dollar didn't go anywhere in Stage 2, since it didn't belong there in the first place (the important figure here is what the clerk kept in Stage 2, not what he kept in Stage 1). To illustrate what I mean, let's look at a more extreme example (that one dollar was missing in the original riddle was not a coincidence... ):

The clerk gets $30 ($10 each) from the friends. He gives them a discount of $10. The bellboy keeps $1 and gives $9 ($3 each) to the friends. Now the friends have spent $21 ($7 each) and the bellboy has $1 in his pocket. 21 + 1 = 22. So where did the other $8 (30 - 22) go? You do the math...

Regards

[Soju]

A suggestion to anyone posting a riddle. Do not use the happy face icon as some of us will think it's a joke rather than a riddle and choose to ignore clicking on it. The only reason why I clicked was because you had the word "riddle" in the title, otherwise I wouldn't have.