"God is not a man, that He should lie, Nor a son of man, that He should repent [nacham]. Has He said, and will He not do? Or has He spoken, and will He not make it good?" (Numbers 23:19) (NKJV)

And it  repented  the  LORD  that he had made man on the earth, and it grieved him at his heart. (Gen. 6:6 KJV)
And the LORD repented [Heb: nacham] of the evil [ra] which he thought to do unto his people. (Exod. 32:14 KJV)
Who knoweth if He [God] will turn and repent, and leave a blessing behind Him? (Joel 2:14 KJV)

This apparent contradiction comes out most strongly in the King James version of the Bible. In the New King James, for example, Genesis 6:6 says, "The Lord was sorry that He had made man on the earth, and He was grieved in His heart.". Again, the word translated "repent" in Joel 2:14 is translated as "relent" in the NKJV.

The word in the Hebrew is the same in all cases however. Thayer's dictionary gives the following information on the word nacham in Hebrew.

05162 nacham {naw-kham'}
a primitive root; TWOT - 1344; v
AV - comfort 57, repent 41, comforter 9, ease 1; 108
1) to be sorry, console oneself, repent, regret, comfort, be comforted
1a) (Niphal)
1a1) to be sorry, be moved to pity, have compassion
1a2) to be sorry, rue, suffer grief, repent
1a3) to comfort oneself, be comforted
1a4) to comfort oneself, ease oneself
1b) (Piel) to comfort, console
1c) (Pual) to be comforted, be consoled
1d) (Hithpael)
1d1) to be sorry, have compassion
1d2) to rue, repent of
1d3) to comfort oneself, be comforted
1d4) to ease oneself

The fact is, ancient Biblical Hebrew had few words and some words had a variety of meanings. There is a range of meaning for "nacham". The Lord is sorry about some things, under certain conditions the Lord relents from doing some things he thinks about doing to punish, but the Lord is not unstable, double-minded, saying one thing and doing the other.

So in Numbers 23:19 we see that God doesn't change his purpose like an unstable man. However, it is a principle that changes in man's basic attitude towards God can occasion God to change what He will do in the case of that person or nation. If we repent of our evil-doing, God may relent from some of the judgments he intended to send on us. If not, God's judgments will certainly stand. "Nacham" can sometimes mean regret, other times it can mean change of action.

To find out what the words of the Bible mean in each of these passages again you have to look at the context. God is not saying one thing and doing another. Yet some of his judgments and blessings are conditional upon our obedience or lack of it.

The fact that God says

"And [at what] instant I shall speak concerning a  nation , and concerning a kingdom, to build and to plant [it];  10  If it do evil in my sight, that it obey not my voice, then I will repent of the good, wherewith I said I would benefit them." (Jeremiah 18:9 KJV).

does not contradict the affirmation of God's integrity in Numbers 23:19.