A simple function for 3 columns.
=SUM(IF(IF(A1:A10<B1:B10,A1:A10,B1:B10)<C1:C10,IF(A1:A10<B1:B10,A1:A10,B1:B10),C1:C10))
A simple function for 4 columns.
=SUM(IF(IF(A1:A10<B1:B10,A1:A10,B1:B10)<IF(C1:C10<C1:C10,C1:C10,D1:D10),IF(A1:A10<B1:B10,A1:A10,B1:B10),IF(C1:C10<D1:D10,C1:C10,D1:D10)))...