A 7-digit base ten positive integer of the form ABCDEFG is called a modified hill number if the digits B, D and F satisfies: B = A + C (mod 10) , D = C + E (mod 10) and F= E + G (mod 10) (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 modified hill number, given that x is a base ten positive integer chosen at random between 1000000 and 9999999 inclusively.

There are 2145 modified hill numbers inclusively between 1000000 and 9999999, therefore there is a 2145/9000000 = 143/600000 ~= 0.000238333 chance that a random number inclusively between 1000000 and 9999999 will be a modified
hill number.

Posted by Dej Mar on 2011-03-10 04:46:58