A 5-digit base ten positive integer of the form ABCDE is called a hill number if the digits B and D are each equal to the sum of the digits to their immediate left and right, that is, B = A + C and D = C + E. (Each of the capital letters in bold denotes a digit from 0 to 9, whether same or different.)

Determine the probability that x is a hill number, given that x is a base ten positive integer chosen at random between 10000 and 99999 inclusively.

There are 330 hill numbers inclusively between 10000 and 99999. The first and last being 11000 and 99099.
There are 90000 numbers inclusively between 10000 and 99999 (99999 - 10000 + 1 = 90000).
Therefore, the probability that a number chosen at random from the set of 90000 numbers is 330/90000 = 11/3000 = 0.00366.

Posted by Dej Mar on 2010-07-15 18:35:26