hardmath

Three people check into a room. The bill is $30. They split it 3 ways. Later on the hotel realizes they should have charged $25 so they send a bellhop to return $5. The bellhop realizes he can't split $5 3 ways to he gives each person $1 and keeps $2. They have now paid $9 each for the room, the bellhop has $2. $27 + $2 = $29 What happened to the last $1 considering $30 was originally paid.

The bellhop has $2. This $2 is covered by the $27 paid by the guests. Don't add it to the $27. The guests have had $3 in total returned to them. $30 - $3 = $27 (of which $2 is the bellhops).

Why this works

This riddle plays with the way we perceive the flow of money and how we add and subtract it. Initially, the guests pay $30, but after the hotel realizes their mistake, they should only have paid $25. The confusion arises when we attempt to add the bellhop's $2 to the $27 that the guests effectively paid ($30 - $3 returned). However, the $27 already includes the bellhop's $2; thus, adding it again creates a misleading total. Instead, think of the $27 as the total amount spent, which accounts for both the hotel and the bellhop's share, leaving the guests with $3 returned.

Common Wrong Answers

“The hotel kept the extra $1.”

The hotel did not keep the extra dollar; they adjusted the bill to $25 and sent back $5 to the guests, which accounts for the total paid.

“The guests overpaid, and the hotel owes them $1.”

The guests did not overpay; they paid $30 and received $3 back, making their effective payment $27 for the room, which is correctly accounted for, with no money owed.

“The bellhop stole the $1.”

The bellhop did not steal the dollar; he returned $3 to the guests and kept $2, which is accounted for in the total payment of $27.

More math riddles →More hard riddles →Browse all riddles →