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The same number of rooks in each column/row | Reply

Can anyone please suggest a smart idea on how to solve this?
If we iterated for each K up to the board size and change the capacities to K then if the maxflow is K*boardsize ( i.e. each column has exactly K rooks ( and therefore each row has exactly K rooks as the flow going out is the flow going in :) ) ) it should be solved, should not it?

Thanks in advance :)