On my way to Philadelphia I pass five mileposts that indicate the distance I still have to travel to Philadelphia. The mileposts are at fixed intervals. Each milepost has a two-digit number, and together the five mileposts use all the digits from 0 to 9 exactly once.

(i) What is the smallest distance that the closest milepost can be from Philadelphia?

(ii) What is the maximum distance that the closest milepost can be from Philadelphia?

***Mileposts don't begin with 0, that is, no milepost can contain a leading zero.

Of the five milepost the smallest distance is the one bearing the distance 10 [98,76,54,32,10], the smallest two-digit non-leading zero decimal number. Of the five mileposts the maximum distance given would be 54 [90,81,72,63,54].

Yet, keeping the stiplulation that the intervals are fixed between all mileposts on the way to Philadephia, there would be additional, yet unpassed mileposts. Assuming there is no 0-miles milepost, the smallest distance before reaching Philadelphia would be the single digit distance of 9 [90,81,72,63,54,(45,36,27,18,9)]; and the maximum distance of the closest of such would be 18 [90,72,54,36,18].

Posted by Dej Mar on 2013-06-01 00:53:18