The missing dollar riddle is a classic brain teaser that can trip up even savvy puzzle solvers:
Three friends split the cost of a hotel room. They are charged $30, so each of them pays $10.
Later the hotel manager realized the room only cost $25 instead of $30. The manager brings $5 to reimburse the friends.
The manager finds it hard to split $5 three ways, so he gives the friends $1 each, and keeps $2 for himself.
But wait – each friend paid $9, for a total of $27, and the manager pocketed $2. That’s 27 + 2 = 29, whereas they originally handed over $30. Where did the missing dollar go?
Solution
There is no missing dollar.
You cannot add the manager’s $2 to the $27 that the three friends paid, because how much they paid already includes it – this would be double-counting. The three friends ended up paying $27, including $25 to the hotel and $2 to the manager, which adds up.
If you want to figure out where the $30 went, you should instead start with the amount that the hotel received ($25), add the amount the manager received ($2), and add the amount the friends received back ($3), which indeed gets you to $30.
Obviously, there is no missing $30. The party has it. In other words, in Scenario (1), we should not add the amount the party pays (i.e., $30 – $3 = $27) to the bellhop’s $2. Rather, we should add the portion the party has of the original $30 (i.e., $30 – $27 = $3) to the portion the bellhop has (i.e., $2) and to the portion the manager has (i.e., $25). This gives $3 + $2+ $25 = $30.