Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 45 less than her favorite number. Also, one digit is one less than double the other digit. What is Sophie's favorite number?
There is no such number. I went through and tried all of the possible numbers, none of them work.
Here is a short way to do so: If the digits are within 4 of each other, then the number's reversal will be too close. However, if they are 6 or above away from each other, the number's reversal will be too far away. So the digits must be 5 apart. Since the first digit must be larger, the possibilities are 50,61,72,83, and 94. None of these match the last requirement, so there is no such number.