MathDB

The numbers

1,2,\ldots,49,50

are written on the blackboard. Ann performs the following operation: she chooses three arbitrary numbers

a,b,c

from the board, replaces them by their sum

a+b+c

and writes

(a+b)(b+c)(c+a)

to 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 san obtain. Find the value of

\frac{A}{B}

.
(I. Voronovich)

Problem Statement