numbers on 3x556 board
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L2 P3
September 19, 2022
combinatorics
Problem Statement
In a board with rows and columns, squares are colored red, one in each of the rows.
If the numbers from to are written in the boxes, in row order, from left to right (in the first row from to , in the second from to and in the third from to ) there are numbers that are written in red squares.
If they are written in the boxes, ordered by columns, from top to bottom, the numbers from to (in the first column from to , in the second from to , in the third from to ,... ., and in the last one from to ) there are numbers that are written in red boxes.
We call red numbers those that in one of the two distributions are written in red boxes.
Indicate which are the squares that must be colored red so that there are only red numbers.
Show all the possibilities.