Question

Please give your answer with complete details.

Answer 1

Answer:

see solution in attachments ....

Answer 2

Answer:

10

Step-by-step explanation:

Easiest trick to solve such questions is to find a pattern :

3 has the following patterns in repeating powers : { 3,9,7,1 }

∴ When the power is divisible by 4 ,it's last digit is always 1.

∴ When the power is divisible by 2 and not 4 it's last digit is always 9.

2016 is purely divisible by 4.

So a = 1.

9018 is not divisible by 4 since 18 is n't so.

So b = 9.

a + b = 9 + 1 = 10.

These solutions won't be written in the book.We need observation,intuition and basic olympiad foundations to solve such problems.