Бамидбар 17:18 Комментарий: Rashi, Or HaChaim, Rabbeinu Bahya & Rav Hirsch

כי מטה אחד FOR ONE STAFF SHALL BE (FOR THE HEAD OF THE HOUSE OF THEIR FATHERS) — i.e. although I have divided them into two families, the family of the priests apart, and that of the Levites apart, yet it is only one tribe, [and they shall therefore have but one staff].

ואת שם אהרון תכתב על מטה לוי, "and you will inscribe the name Aaron on the rod of the tribe of Levi." The Torah had to mention this as it had not previously written that the tribe of Levi was one of the 12 tribes for whom rods were to be taken. [Menashe and Ephrayim could have made up the tribe of Joseph. Ed.] It is possible that the whole procedure was that they took one long rod and divided it into 12 equal lengths and every tribal head came and took one length of the same original rod. In that way the test was absolutely fair as all the parts of that rod had come from the same root. If this was the procedure we can also understand the meaning of the words ומטה אהרון בתוך מטותם, "that the rod of Aaron was a part of their rods" (verse 21). I have found an opinion quoted in Bamidbar Rabbah 18,23 which confirms what I have just written.

כי מטה אחד לראש בית אבותם, For there shall be one staff for each head of an ancestral house - meaning that even though the tribe was divided between Preistes and Levites, [they were still] one staff for the head of their ancestral house.