Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist LR2 day1 (Logic Reasoning)

Tags: combinatorics



In the rectangle in the figure, we are going to write $12$ numbers from $1$ to $9$, so that the sum of the four numbers written in each line is the same and the sum of the three is also equal numbers in each column. Six numbers have already been written. Determine the sum of the numbers of each row and every column.