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The column-wise reduction matrix is shown in the following table.
Leave the elements covered by single line as it is. Take any row or column which has a single zero and assign by squaring it.
Strike off the remaining zeros in that column or row, and repeat the same for other assignments also.
If there is no single zero allocation, it means multiple numbers of solutions exist.
Problems related to assignment arise in a range of fields, for example, healthcare, transportation, education, and sports.
In fact, this is a well-studied topic in combinatorial optimization problems under optimization or operations research branches.