Three men went to a hotel to rent a room, the cost of the room was $30. Each man paid $10 to the bellboy and proceeded to their room. After a little while the bellboy realized that there was a special on rooms that night and the price for the men's room should have been $25. On his way to the men's room to give them back $5, he was puzzled how he was going to split $5 as he had no change. He decided he would give them each $1 and keep the remaining $2 for himself. So each man originally paid $10, but after the bellboy gave each man $1 back, each man paid $9. 9 x 3 = $27 plus the $2 the bellboy put in his pocket equals $29. The original price for the room was $30. Where did the last dollar go? Which shows that even though something sounds logical, it might not be. There is no "last dollar". There is a fallacy in the thought process and calculations. The $2 should be subtracted from the $27 to show what ended up being paid for the room. Or $30 - $1 - $1 - $1 - $2 = $25 Probably the most difficult recently solved problem was Fermats enigama. Which involved cubes. It has taken many years and the consolidation of the work of dozens of people to resolve.
That's a pretty nice puzzle anonymous. Had me stumped for a little bit.