Hi, My question is related to a math puzzle. The puzzle asks to swap any two digits from the numerator with any two digits in the denominator of the fraction 1630 / 4542 to get the ratio 1 / 3. Two possible answers are 1534 / 4602 and 1354/ 4062. What I am struggling with is the number of possible combinations we would have if we were to use brute force to solve this problem. The solution of the problem says that there are 8! (i.e. 40,320) possible combinations. My analysis gets me only 144 combinations. Here is my analysis :There are 12 ways to pick a pair from the numerator and there are 12 ways to pick a pair from the denominator. A pair from the numerator can replace any one of the 12 pairs in the denominator. As a result there are 12x12 =144 combinations. What am I missing? Thank you.