document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208628>Question 1208628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number? </SPAN>\n" );
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document.write( "The problem is faulty.  There is no 2-digit number that satisfies both conditions.<br><BR>\n" );
document.write( "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><BR>\n" );
document.write( "Let the 2-digit number be \"AB\"<br><BR>\n" );
document.write( "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><BR>\n" );
document.write( "(10A+B)-(10B+A) = 9A-9B = 9(A-B)<br><BR>\n" );
document.write( "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><BR>\n" );
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