Three friends decide to split the cost of hiring a cleaner. The agency charges them $30, so they each hand over a $10 bill.
Later the agency discovers the rate was actually $25 instead of $30. They send the cleaner with $5 to reimburse the friends.
It’s hard to split $5 three ways, reasons the cleaner, so he gives the friends $1 each, and keeps $2 for himself as a tip.
But wait – each friend paid $9, for a total of $27, and the cleaner pocketed $2. That’s 27 + 2 = 29, whereas they originally handed over $30. Where did the missing dollar go?
The missing dollar riddle is a classic, well-known riddle of unclear origin – usually with a clerk and a room bill or a waiter and a restaurant bill. But it’s simple yet tricky, and may trip up even savvy puzzle-solvers.
Solution
There is no missing dollar.
You cannot add the cleaner’s $2 “tip” to the $27 that the three friends paid, because how much they paid already includes that tip – this would be double-counting. The three friends ended up paying $27, including $25 to the agency and $2 to the cleaner, which adds up.
If you want to figure out where the $30 went, you should instead start with the amount that the agency received ($25), add the amount the cleaner received ($2), and add the amount the friends received back ($3), which indeed gets you to $30.