Question 1208628
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The problem is faulty.  There is no 2-digit number that satisfies both conditions.<br>
For any 2-digit number, the difference between that number and the number with the digits reversed is always 9 times the difference between the two digits.  Formally....<br>
Let the 2-digit number be "AB"<br>
The value of the 2-digit number is 10A+B; the value of the number with the digits reversed is 10B-A.  The difference between the two numbers is<br>
(10A+B)-(10B+A) = 9A-9B = 9(A-B)<br>
In this problem, with a difference of 72 between the two 2-digit numbers, the difference between the two digits is 72/9 = 8.  That means the two digits must be 1 and 9, making Sophie's favorite number 91.  But that number doesn't satisfy the other given condition.<br>