This is a problem for a number theory classSolutionLet us su

This is a problem for a number theory class

Solution

Let us suppose that N is any 4 digit number such that N=abcd, where a,b,c and d are the digits at thousand\'s, hundred\'s and tenth and unit digit respectively.

Therefore,N=1000*a+100*b+10*c+d

If we reverse the order of digits in N, we get M=dcba, where d,c,b and a are the digits at thousand\'s, hundred\'s and tenth and unit digit respectively.

Therefore M=1000*d+100*c+10*b+a

N-M=999*a+90*b-90*c-999*d

Therefore, N-M has 9 as its factor for sure and hence is divisible by 9.

This can be verified for any integer with any number of digits.