1981 AHSME Problems/Problem 16
Problem
The base three representation of 
is
![\[12112211122211112222\]](http://latex.artofproblemsolving.com/1/9/e/19ee9a81d71f36177bfbd8f9886022b1ae264e14.png)
The first digit (on the left) of the base nine representation of is
Solution (Long Way)
Convert to base 10 then convert the result to base 9.
![\[12112211122211112222_{3} = 2150029898\]](http://latex.artofproblemsolving.com/6/4/e/64ebb09efcb51d16c956f98d227a8502de88a8b0.png)
![\[2150029898 = 5484584488_{9}\]](http://latex.artofproblemsolving.com/9/d/e/9ded47e3858d6a4a0d1be36ac3ce6e923e00ac6f.png)
Therefore, the answer is 
-edited by coolmath34
Solution (Faster Way)
Every 2 numbers in base 3 represents 1 number in base 9. The first 2 numbers on the left,12 = 1(3) + 2(1) = 5.
So the answer is
