# Article

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Keywords:
necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program
Summary:
Modifications to a procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem are described. These modifications reduce the computation required to such an extent that necessary and sufficient conditions for the existence of a solution to the 3x3x3 multi-index problem can now be determined. These conditions are given in this paper.
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