A Set Problem and a Sum Problem
I'm not sure what category these belong in. They're somewhat like puzzles.
1. In a certain town, there live exactly 100 men. 85 are married, 70 have a cell phone, 75 own a car, and 80 own a house. What is the smallest possible number of men who do all four (married, have cell phone, own car, own house)?
I got an answer for that but I'm looking for a more formal way of doing it.
2. Find all the positive integers n such that 1! + 2! + ... + n! is the square of a positive integer, for n >= 3