Problem:
The base three representation of x is
12112211122211112222.
The first digit (on the left) of the base nine representation of x is
Answer Choices:
A. 1
B. 2
C. 3
D. 4
E. 5
Solution:
Grouping the base three digits of x in pairs yields
x=(1⋅319+2⋅318)+(1⋅317+1⋅316)+…+(2⋅3+2)=(1⋅3+2)(32)9+(1⋅3+1)(32)8+…+(2⋅3+2).
Therefore, the first base nine digit of x is 1⋅3+2=5.