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 five-digit numbers between 10000 and 99999 which meet the definition, so the probability is 330/90000 or .0036666...

Posted by ed bottemiller on 2010-07-15 13:58:28