Abstract: Various methods have been proposed for off-line permutation packetrouting on a mesh. One of the methods is known as multistage routing, inwhich the first stage is crucial. For the first stage of routing, theprevious study normally converts it to a problem of graph theory and provesthe existence of solutions. However, there is a lack of simplealgorithms to the first stage of routing. This article presents anexplicit and simple approach for the first stage of routing based onelementary mathematics.