Find the number of three-digit numbers from 100 to 999 including all numbers which have any one digit that is the average of the other two.

Explanation

Alternate solution :
Consider two sets.
(i) 1,3,5,7,9
(2) 0,2,4,6,8
The required number of ways =[any two from set (1)+ any two from set (2) (excluding zero)]=3!+[0 along with any one from set `(2)]xx4`+all three alike
`=(""^(5)C_(2)+""^(4)C_(2))xx3!+ ""^(4)C_(1)xx4+9=121`