Question 149
The numbers $1, 2, \dots, 49, 50$ are written on the blackboard. Ann performs the following operations: she chooses three arbitrary numbers $a, b, c$ from the board, replaces them by their sum $a + b + c$ and writes the number $(a + b)(b + c)(c + a)$ into her notebook. Ann performs such operations until only two numbers remain on the board (in total 24 operations). Then she calculates the sum of all 24 numbers written in the notebook. Let $A$ and $B$ be the maximum and the minimum possible sums that Ann can obtain.
Find the value of $\frac{A}{B}$.
Find the value of $\frac{A}{B}$.