Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37!	Select
A) 2  B) 4  C) 6  D) 8  E) 0
3,8 and 7 have a power cycle of 4, i.e. the units digit in each case will repeat after every 4th power.   For eg : 3^1 = 3, 3^2 = 9 , 3^3 = 27 , 3^4 = 81, 3^5 = 243   All the powers given(1!+2!+....), are multiples of 4. It is so because the last 2 digits of the total sum will be 00,for each one of them, which make them divisible by 4.   Thus, the given problem boils down to 3^4+8^4+7^4=1+6+1= 
<gadget id="calculator">1+6+1</gadget>
<output>8</output>
8   Thus, the units digit is 8.   ANSWER:8
<result>D</result>
Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37!