Without referring to the many solutions available on the web (BINGO! is very popular):
1) What is the expected value of the number of numbers that must be "called" to reach a BINGO! on a single card?
2) What if you are allowed to play 5 cards (presumably all different)?
Also, usually the center square of the grid is "free", i.e. it is assumed to be called already at the beginning of the game.
3) What are the resulting values for Questions 1) and 2) in this case?
Extra hard bonus:
There are many many variations of the game that allow changes to the pattern of numbers/grid spaces that must be "called" to reach a BINGO! A "+" and an "X" are two of these. Both require 8 numbers to be called, assuming there is a free space in the middle. What are the expected values of the number of numbers "called" for each of these?
The author admits that computer solutions are very viable to solve this problem, but BINGO! existed long before computers. Any analytical attempts/solutions get bonus points!