This Bible contradiction is from the Skeptic's Annotated Bible.
Yes, certain kinds of tests are okay.
Judges 6:36-40 View context
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.
1 Kings 18:36-38 View context
And it came to pass at [the time of] the offering of the [evening] sacrifice, that Elijah the prophet came near, and said, LORD God of Abraham, Isaac, and of Israel, let it be known this day that thou [art] God in Israel, and [that] I [am] thy servant, and [that] I have done all these things at thy word.
Hear me, O LORD, hear me, that this people may know that thou [art] the LORD God, and [that] thou hast turned their heart back again.
Then the fire of the LORD fell, and consumed the burnt sacrifice, and the wood, and the stones, and the dust, and licked up the water that [was] in the trench.
2 Kings 20:8-11 View context
And Hezekiah said unto Isaiah, What [shall be] the sign that the LORD will heal me, and that I shall go up into the house of the LORD the third day?
And Isaiah said, This sign shalt thou have of the LORD, that the LORD will do the thing that he hath spoken: shall the shadow go forward ten degrees, or go back ten degrees?
And Hezekiah answered, It is a light thing for the shadow to go down ten degrees: nay, but let the shadow return backward ten degrees.
And Isaiah the prophet cried unto the LORD: and he brought the shadow ten degrees backward, by which it had gone down in the dial of Ahaz.
No, God doesn't like to be tested or tempted.
Deuteronomy 6:16 View context
Ye shall not tempt the LORD your God, as ye tempted [him] in Massah.
Matthew 4:7 View context
Jesus said unto him, It is written again, Thou shalt not tempt the Lord thy God.
Luke 4:12 View context
And Jesus answering said unto him, It is said, Thou shalt not tempt the Lord thy God.