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?

broll probably has the solution you want since without a reset the first solution uses an extra space on the trip odometer.
Without hitting the reset button the trip odometer quickly outpaces the regular one.  So we need to travel over 1000 miles until they approach again:
Let backtrack to where the button was last pushed
Regular  Trip   Elapsed
12222.2 0.0  (-123.4)
then run forward
13522.2 1300.0 (1176.6) Here they share the first 2 digits.
13574.2 1352.0 (1228.6) Here they share the first 3 digits.
13579.2 1357.0 (1233.6) Here they share the first 4 digits.
13580.2 1358.0 (1234.6) Here they share the first 5 digits.

With my interpretation it is unclear whether you want to just match the first 4 digits (answer=1233.6) or the entire display of the trip odometer (answer=1234.6)

Posted by Jer on 2013-03-26 12:49:55