(A) Determine all possible value(s) of a 2-digit non leading zero base nine positive integer x such that we will obtain a remainder of x, whenever 2^x is divided by the base nine number 100. What are the possible values of x - if a remainder of x is obtained, whenever 5^x is divided the base nine number 100?

(B) Determine all possible value(s) of a 2-digit non leading zero base eleven positive integer y such that we will obtain a remainder of y, whenever 2^y is divided by the base eleven number 100. What are the possible values y- if a remainder of y is obtained, whenever 5^y is divided the base eleven number 100?

*** For an extra challenge, solve this problem without using a computer program.