2016/031) Find 3 digit number which is same as sum of factorials

Let the number be $100 a + 10b+c$
none of $a,b, c$ can be $> 5$ as $6! = 720$ and $7! = 5040 > 1000$
one of them that is b or c= 5 ( a cannot be 5 as $5! = 120$ and $5! + 4! + 3! < 200$)
so $a = 1, b= 5, c = ?$ or $a = 1, b = ? , c = 5$ ( it has to be $< 5$)
if  $a = 1 , b = 5$ we get $1 + 120 + c ! > 150$ and $< 160$
$39 >c! > 29$ and so there is no c
if $a = 1, c = 5$ we get $1 + 120 + b! = 105 + 10 b$
so b = 4 and the number is 145