Find the Heavier Ball Puzzle

You have 9 balls, equally big, equally heavy - except for one, which is a little heavier.

How would you identify the heavier ball if you could use a pair of balance scales only twice?

The Missing Dollar Puzzle

Three people check into a hotel. The clerk tells them that the bill for their stay is $30, so each person pays the clerk $10. The clerk puts the money in the cash register.

Later that night, the clerk realizes that he made a mistake and should have only charged the three guests $25. He pulls $5 in one dollar bills out of the register and tells the bellhop to return the money to the guests.

On the way to the room, the bellhop realizes that he cannot split the money evenly between the three people. As the guests don't know that they were charged the incorrect amount for their room, the bellhop decides to simply give them $1 each and pocket the extra $2 as a tip. Each guest gets $1 back, so they each paid $9 for their room, totaling $27. The bellhop kept $2, and $27 + $2 = $29.

But the guests originally handed over $30. What happened to the missing dollar?