No fours
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
The answer is 1462.
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1 solution
Since the odometer is lacking 1 of the digits to be a natural number in base 10, it basically work with a base 9 numbering. The real mileage is 2*9^3 + (5-1) = 1462. Minus 1 because the 5 has already "skipped" the last 4.