The sum of the digits of a two digit number is fourteen if the number represented by reversing the digits is subtracted from the original number the result is eighteen what is the original number?

Answer 1

86 8 + 6 = 14 86 - 68 = 18 The difference of a transposition (reversing the digits), is always divisible by 9. If you take the difference, in this case 18, and divide that by 9, your answer is 2. This will be the difference between the two digits (ie, 1 + 2 = 3, so transposing 13 and 31 results in a difference of 18. So does 24 and 42 or 35 and 53, etc). This helps you quickly solve the problem by taking one half of the sum of the digits (14), divide in half (7) and move 1 number in each direction (one being half of 2, the known difference between the digits) and you get 8 (7+1) and 6 (7-1). If your difference was 27, then the two digits would be 3 numbers apart (27 divided by 9 = 3) such as 14 and 41 or 25 and 52, etc. If the solution was 25 and 52: The two numbers add to 7 and the difference of the transposition is 27. The two numbers add to 7 - one half of 7 is 3.5 - move 1.5 (half of 3, 27/9) in either direction from 3.5 and you get your answer 5 (3.5+1.5) and 2 (3.5-1.5). Try it where the difference of the transposition is 36 (the difference in the digits will be 4) such as 37 and 73 or 48 and 84.