Saul was driving to work one day, when he glanced at his car's dashboard and noticed something interesting about his mileage indicators. His odometer, which shows the miles driven since the car was manufactured, hit 12,345.6 miles, and his trip meter read 123.4 miles. So, the meter matches the first four digits on the odometer.

(i) How far must Saul drive - before this happens again?

(ii) What is the smallest distance that Saul can drive so that the two odometers have all ten digits between them, but share no digits in common?

12345.6 123.4 (0)
12374.4 152.2 (28.8)
Press button
12374.4 0 (28.8)
12678.9 304.5 (333.3)

This has an elapsed distance of 333.3 miles, found by working backwards.  (I'm pretty sure but not positive it cannot be improved.)

Without pressing the reset button I've gone past 400 miles with no solution.

Posted by Jer on 2013-03-26 14:08:40