AMC 12: 2005 #19

Here's a nice little problem I did yesterday. The problem was that I did this problem the (relatively) long way compared to the elegant solution.

$A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. If the odometer now reads 002005, how many miles has the car actually traveled?$

Solutions (Highlight to reveal):

Just convert 2005 to base nine! Notice there's a one-to-one correspondence between {0,1,2,3,5,6,7,8,9} and {0,1,2,3,4,5,6,7,8}. So therefore the answer will be 1462.

-runiteking1