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?

(In reply to Part 1 only by broll)

The simplest approach is 12345.7+x=100x,  12345.7=99x, where x=124.7 miles.

This solution won't work because the trip odometer increments by 1 not 100.

12345.6+124.7 = 12470.3
123.4+124.7 = 248.1 these don't start with the same digits.

Or do you mean Saul presses the button to reset the trip odometer?
That works.  Sneaky.

Posted by Jer on 2013-03-26 12:37:12