The Missing Euro

“Three guests check into a hotel room. The clerk says the bill is €30, so each guest pays €10. Later the clerk realizes the bill should only be €25. To rectify this, he gives the bellhop €5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest €1 and keep €2 for himself.

Now that each of the guests has been given €1 back, each has paid €9, bringing the total paid to €27. The bellhop has €2. If the guests originally handed over €30, what happened to the remaining €1?”   ^source

Solution

This is a sneaky misdirection, one that's easy to be fooled by because of the specific numbers chosen for this riddle. In reality this is not how you would add it all up. To get to €30 it goes like this: the clerk takes €25, the bellhop takes €2, and the guests get a €3 refund. It adds up just fine.

Here is the flow of cash. No-one will deny that the total never differs from 30 euros.

	Guest #1	Guest #2	Guest #3	Clerk	Bellhop	Total
Before check-in	10	10	10	0	0	30
After check-in	0	0	0	30	0	30
Before ‘refund’	0	0	0	25	5	30
After ‘refund’	1	1	1	25	2	30