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Deut. 6:16 Ye shall not tempt the LORD your God, as ye tempted him in Massah.
Judges 6:36-40 And Gideon said unto God, If thou wilt save Israel by mine hand, as thou hast said, Behold, I will put a fleece of wool in the floor; and if the dew be on the fleece only, and it be dry upon all the earth beside, then shall I know that thou wilt save Israel by mine hand, as thou hast said. And it was so: for he rose up early on the morrow, and thrust the fleece together, and wringed the dew out of the fleece, a bowl full of water. And Gideon said unto God, Let not thine anger be hot against me, and I will speak but this once: let me prove, I pray thee, but this once with the fleece; let it now be dry only upon the fleece, and upon all the ground let there be dew. And God did so that night: for it was dry upon the fleece only, and there was dew on all the ground.
Did Gideon violate Deut. 6:16, and did God just let it pass?
Let's look at the word behind "tempt" -- nacah. It has a fairly broad application, and by some of these definitions, it may be argued that Gideon did nacah God in violation of Deut. 6:16. But the key is to look at what Deut. 6:16 refers to--an event at Massah. This event is recorded at Exodus 17:1-7--
And all the congregation of the children of Israel journeyed from the wilderness of Sin, after their journeys, according to the commandment of the LORD, and pitched in Rephidim: and there was no water for the people to drink. Wherefore the people did chide with Moses, and said, Give us water that we may drink. And Moses said unto them, Why chide ye with me? wherefore do ye tempt the LORD? And the people thirsted there for water; and the people murmured against Moses, and said, Wherefore is this that thou hast brought us up out of Egypt, to kill us and our children and our cattle with thirst? And Moses cried unto the LORD, saying, What shall I do unto this people? they be almost ready to stone me. And the LORD said unto Moses, Go on before the people, and take with thee of the elders of Israel; and thy rod, wherewith thou smotest the river, take in thine hand, and go. Behold, I will stand before thee there upon the rock in Horeb; and thou shalt smite the rock, and there shall come water out of it, that the people may drink. And Moses did so in the sight of the elders of Israel. And he called the name of the place Massah, and Meribah, because of the chiding of the children of Israel, and because they tempted the LORD, saying, Is the LORD among us, or not?
It is clear from this example that the command of Deut. 6:16 has to do with nacahing God in a very specific way: That is, by a sort of open defiance and rebellion that denies the presence of the Lord. In contrast, Gideon's request (note particularly his trepidation in v. 39, which may indicate an awareness of verging on the "testing" prohibition) was the humble request of one insecure and unsure of his place.
Indeed, as Rihbany shows in The Syrian Christ  this is merely an example of Oriental intimacy and unreserve, which seeks affectionate assurance even the dearest friends. "Especially when new confidences are exchanged or great favors asked, a man turns to his trusted friend and says, 'Now you love me; I say you love me, don't you?' 'My soul, my eyes,' answers the other, 'you know what is in my heart toward you; you know what the Creator knows!' Then the request is made." Rihbany points to the comparison of Peter before Christ around the fire in John 21.
So did Gideon lack faith (loyalty) here? Yes, but he wasn't openly rebelling against God's authority: he was asking for confirmation of what that authority wanted. There is no indication that he doubted that the Lord was with him, as the people did at Massah; what is indicated is that he was unsure of what the Lord wanted him to do. (Note that in Matt. 4:6-7, where Jesus puts Deut. 6:16 to Satan in reply to Satan's temptation to leap from the Temple, what is suggested amounts to an open rebellion against God's will and authority.)