Question

A nine digit number has all its digit except 7 . the sum of the first 4 equals the sum of the last four and the sum is an integral multiple of the middle digit...what is the middle digit

Answer 1

Step-by-step explanation:

_____18___2____18_____

in this diagram I want to show that the middle digit is 2 . becouse 18 is integral multiple of 2

again,

sum of all 9 digits except 7= 9×10/2-7= 38

sum of first four digits+ sum of last 4 digits +

middle digit = 38

since sum of ( first 4= last4 )

=> 2× sum of first 4 digit+ middle= 38

=> sum of first 4 + middle/2 = 19

=> middle digit is even no.

=> sum of first 4 digit is also even.

becouse it is multiple of middle digit

by law of induction we put 2, 6 at

middle digit the result found it is = 2