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The crack technique is the following:
1) M is A tens plus B units, then M=10*A+B;
2) N is B tens plus A units, then N=10*B+A;
3) M+N=(10*A+B)+(10*B+A)=11*A+11*B=11*(A+B)
4) so the sum of M and N must be divisible by 11.

How to reveal the right answer since now is easy, isn't it?

The all answers except for 181 are divisible by 11.