My lousy car has an odometer without 4s — in every position, the counter advances from 3 directly to 5.
For example, when it read 000039 I drove one mile and watched it roll over to 000050.
Today the odometer reads 002005.
How many miles has the car actually traveled?
Source: 2005 American Mathematics Competition
It's a variant of base 9, but with some of the characters changed: 5=4, 6=5, etc.
So there are 2*9^3+4 miles, or 1462 miles travelled.
Posted by broll
on 2016-06-02 08:13:37