Find the last two digits of the following sum: $$5! + 6! + 7! + 8! + \cdots + 100!$$
+191 to solve this problem, adding everything together would be far too slow.
As a faster solution, I suggest figuring out the last two digits for every value and finding a pattern.
5! = 120
6! = 720
7! = 5040
8! = 30240
9! = 362880
10! = 3628800
11! = 39916800
and as we can observe, all the rest all ends in 00
the answer: 20+20+40+80= 160, and we want the last two digits, which are 60
