A Bible Puzzle About the Staff of Moses and Aaron
The idea that one staff could be the staff of Moses, Aaron and God is perfectly biblical.
Exodus 4:2; 7:15, 20; 9:23; and 10:13 all refer to Moses’ staff or rod, that was used to perform signs and wonders. But Exodus 7:10, 12, 19 and 8:1, 12 describe Aaron as possessing this staff and performing the miracle of the rod turning into a snake. Moreover, Exodus 4:20 states: “in his hand Moses took the rod of God” (RSV; cf. 17:9). Are these “contradictions”? No.
I would say, “why must we necessarily choose?” It could refer to one and the same. It has to be understood also that Aaron functioned as Moses’ assistant or representative:
Exodus 4:10-16 (RSV) But Moses said to the LORD, “Oh, my Lord, I am not eloquent, either heretofore or since thou hast spoken to thy servant; but I am slow of speech and of tongue.”  Then the LORD said to him, “Who has made man’s mouth? Who makes him dumb, or deaf, or seeing, or blind? Is it not I, the LORD?  Now therefore go, and I will be with your mouth and teach you what you shall speak.”  But he said, “Oh, my Lord, send, I pray, some other person.”  Then the anger of the LORD was kindled against Moses and he said, “Is there not Aaron, your brother, the Levite? I know that he can speak well; and behold, he is coming out to meet you, and when he sees you he will be glad in his heart.  And you shall speak to him and put the words in his mouth; and I will be with your mouth and with his mouth, and will teach you what you shall do.  He shall speak for you to the people; and he shall be a mouth for you, and you shall be to him as God.
Aaron was Moses’ “prophet” (Exodus 7:1) and working associate (Exodus 4:27-30). Hence, the phrase “Moses and Aaron” appears 64 times in the RSV, in the [Protestant 66-book] Old Testament: all but five of these instances in Exodus, Leviticus and Numbers.
It’s not unbiblical or “un-Hebraic” at all for the Bible to refer to creatures as representatives of other creatures or of God himself. The angel of the LORD is a prime example of the latter (See Genesis 31:11-13; Exodus 3:2-4; Judges 2:1; 13:3-22). We also see an equation of God’s work and the work of men who follow Him (“both/and”), in St. Paul and the Gospel of Mark (Mark 16:20; 1 Corinthians 3:9; 15:10, 58; Ephesians 2:10; Philippians 2:12-13).
Because of this sort of “both/and” thinking, the idea that the staff or rod could be both Moses’ staff and God’s (and/or also Aaron’s) at the same time is perfectly biblical. God calls this staff of Moses “your rod” (Exodus 14:16) and he also refers to “the rod of Aaron” (Num 17:10; cf. 17:6, 8).
If Moses can be God‘s “mouthpiece” then by the same token and by analogy, Aaron could be Moses’ mouthpiece and act on his behalf as a representative, with his rod. No problem; no “contradiction.” Nor is it a contradiction later on when Moses habitually acts on his own, with the staff, or rod (Exodus 9:23; 10:13; 14:16 cf. 14:21, 26-27).
When God says to Moses, “you shall say to him…” (7:16), it’s understood that this could or would include Aaron as his spokesman (4:15-16). In case anyone misses this aspect, God specifically tells Moses to “Say to Aaron” [the same stuff God told him to do] (7:19).
Then the text summarizes that they worked in concert (“Moses and Aaron did as the LORD commanded…”: 7:20). It’s fascinating that after mentioning both, the text states, “he lifted up the rod…” We can’t immediately tell which one did it. But the context of 7:19 strongly suggests that Aaron did: according to his role as assistant.
The same thing happens in the next chapter. God told Moses to warn Pharaoh of the plague of frogs (8:1-4). Then God tells Moses to tell Aaron to stretch out his hand, to cause the plague to start (8:5-6). It’s a joint effort.
Exodus 9 continues the notice of joint effort. God sometimes says what he says to Moses alone (9:1, 12-13, 22), and also sometimes to “Moses and Aaron” (9:8). When God speaks to only one of them; it’s almost always to Moses, as the leader. Then it’s reported that “Moses said to Aaron” (16:9, 33; 32:21). The only time God speaks directly to Aaron alone in the book of Exodus, he says, “Go into the wilderness to meet Moses” (4:27).
The same pattern holds in Leviticus. It’s always Moses telling Aaron what God told him, except one time, where God is instructing Aaron of his duties as high priest, which is a different function altogether: one that he alone does, and not Moses (see Exodus 10:8-11). Even then, Moses informs Aaron of additional instructions (10:12-15).
All of this is simply taking the Bible at face value, on its own terms. But prior “critical” bias interferes with that goal, and so, too often, only “sees” supposed contradictions.