Missing Dollar Puzzle

Three men go to a hotel. The desk clerk gives them a room for $ 30, so each one pays $ 10 and they occupy the room. Later, the desk clerk realizes the room had a off-season discount of $ 5 and should cost only $ 25, so he sends the bellboy to the three guys room with $ 5. On the way, the bellboy couldn't figure out how to split $ 5 evenly between three men, so he gives each one $ 1 and keeps the other $ 2 for himself.

This meant that each man paid $ 9 for the room, which is a total of $ 27. And the bellboy kept $ 2, so the total becomes $ 29. Then where is the other dollar?

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Solution:

This particular puzzle stumps many people because it forces the mind to think in the wrong direction. In fact the wrong solution is offered in the puzzle itself to make the mind stop looking for a logical solution. But what you need to do is look at the situation with a fresh mind and ignore what has been told to you.

1) Three men start out with $10 each ($10 x 3 = $30). Fine

2) Three men pay $30 for a hotel room. Afterwards, a five dollar overcharge is returned to them ($25 + $5 = $30). So far so good.

3) The bellboy divides up the $5 overcharge, returning $1 to each of the three men (for a total of $3) and keeping $2 for himself ($25 + $3 + $2 = $30).

4) The bellboy keeps $2 for himself, so effectively each man pays $9 ie (($25 + $2)/3), so the total amount paid is $27

5) The bellboy returns $3 to the three men ie $27 + $3 = $30


The question asked is where did the missing dollar go? But in the first place the dollar did not go missing. One is forced to thinks that the dollar goes missing because the statement "each man paid $9 for the room" has been told in the puzzle itself and that is wrong — each of three men paid out a total of $9, but that $9 included both the room charge and the bellboy's tip. All in all, each man paid out a total of $9 and had $1 left over, completely accounting for the $30 they started with.

The room cost $25, so each man paid one-third of that cost ($8.33). The bellboy kept a tip of $2, so each man paid one-third of that cost ($0.67) as well. Overall, each man paid out $9 ($8.33 + $0.67) and had a dollar left over: (3 x $9) + (3 x $1) = $27 + $3 = $30.