What is the remainder when $1! + 2! + 3!$ + … + 100! is divided by 12?

Explanation

1. 01

   From $4! = 24$ onwards every factorial is a multiple of 12.

2. 02

   So only $1! + 2! + 3! = 1 + 2 + 6 = 9$ matters.

3. 03

   9 is less than 12, so the remainder is 9.