Question 1209008
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Sophie's favorite number is a two-digit number. If she reverses the digits, the result is $45$ less 
than her favorite number. The sum of the digits in her favorite number is $6$. What is Sophie's favorite number?
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The given info that the difference of the number and the reversed number is  45
tells us that the difference of the digits is  45/9 = 5.


Hence,  the digits are of different parity.


Then the sum of the digits can not be  6.    Contradiction.



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