Arrangement of an n x n table with entries in {0, 1}.
Source: Tuymaada 2004, day 2, problem 3. - Author : O. Vanyushina.
May 25, 2007
vectorfunctioninductioncombinatorics proposedcombinatorics
Problem Statement
Zeroes and ones are arranged in all the squares of table.
All the squares of the left column are filled by ones, and the sum of numbers in every figure of the form
[asy]size(50); draw((2,1)--(0,1)--(0,2)--(2,2)--(2,0)--(1,0)--(1,2));[/asy]
(consisting of a square and its neighbours from left and from below)
is even.
Prove that no two rows of the table are identical.Proposed by O. Vanyushina