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 twodigit 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 twodigit nonleading 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 0miles 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 20130601 00:53:18 