1,995 soldiers lined up in a column
Source: I Soros Olympiad 1994-95 Ukraine R2 9.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 6, 2024
combinatorics
Problem Statement
On the square, soldiers lined up in a column, and some of them stood correctly, and some turned backwards. Sergeant Smith remembers only the command "as". With this command, each soldier who sees an even number of faces facing him turns , while the rest remain stationary. All movements on command are performed simultaneously. Prove that the sergeant can orient all the soldiers in one direction.