nice problem from today's math competition I'm probably allowed to share
there's a 2025x2025 grid filled with integers
* you know the sum of each row and the sum of each column (labeled); prove you can't reconstruct the table
* you know the sum of each orthogonal pair (labeled) and the total sum of the grid; prove you can reconstruct the table
* you only know the sum of each orthogonal pair (still labeled); can you reconstruct the table?