Some puzzles do not hide a difficult calculation, but a badly framed sum. Everyone here knows how to add, yet almost everyone adds things that should not be added.
The Ever-Missing Euro
Riddle statement
Three friends pay 30 € for dinner.
Each contributes 10 €.
Later, the waiter realizes that the real bill was 25 €, so he gives 5 € to the assistant to return to them.
The assistant gives 1 € back to each friend and keeps 2 €.
Now each friend has paid 9 €. Together, the three have paid:
The assistant has 2 €.
Where is the missing euro?
Show solution
Solution
No euro is missing.
The friends initially put down 30 €.
Then they received 3 € back, one for each friend.
So together they really paid 27 €.
But those 27 € already include everything:
25 € went to the restaurant; 2 € were kept by the assistant.
Therefore:
The incorrect sum is:
because those 2 € are already included in the 27 € paid.
The correct accounting is to add the 25 € bill, the 2 € kept by the assistant, and the 3 € returned:
Answer: no euro is missing. The trick is that the assistant's 2 € are being counted twice.