Regarding foreknowledge, I find it inconceivable and impossible to explain how, according to the traditional doctrine of God's foreknowledge, God can know from the beginning who will be saved and who will not be saved while at the same time both of the latter have a free will in choosing their destiny. I'm open to hearing someone else explain this but after 25 years of trying to come to a Biblical and logical answer, I find none. Perhaps you can help?

Thank you for your question. It is a question that has puzzled many and I cannot guarantee that I can bring any satisfaction. In fact, if you have been seeking for an answer for 25 years, I have to admit I have little hope of satisfying your puzzlement. However, that has not stopped me before. I will try my best to help. If it does not, then at least I have tried.

First, let us establish two definitions and then try to determine the possible relationships between these two ideas. Since we have to begin somewhere, I will use my own definitions. The two words are foreknowledge and foreordination. I define foreknowledge as God’s perfect knowledge of the future. I will define foreordination as God’s ordering of future events so that they are absolutely determined by His will. Even if you disagree with my definitions, this will give us a basis for discussing the subject.

The problem many have is how foreknowledge can be absolute while foreordination is not (thus allowing for a level of free will). The thinking, if I understand it correctly, goes like this. For an illustration, let's imagine a man who we will call John and then give him a decision to make. For the sake of simplicity, we will say that he only has two possible choices which we will label choice A and choice B. John has no idea which he will choose but feels inwardly that he has complete power over the choice and can freely choose either A or B. However, God because of His foreknowledge already knows what choice John will make. He knows that John will in the end choose B. This is absolute knowledge and it will definitely happen. So, does John have a free will to choose either A or B as he feels or is he predetermined to choose B no matter what since this is what God knows will indeed happen? That is, is John foreordained to do what God knows he will do? This is a truly difficult problem. However, before we finish with John, let's consider three possible relationships between foreknowledge and foreordination.

1. Some teach that God foreknows all future events because He has foreordained all future events. In this view, the two concepts cannot be separated. God’s foreknowledge is the same as His foreordination. This doctrine denies the reality of man’s free will and makes salvation a matter of God’s arbitrary choice (called unconditional election). Despite attempts to avoid this by most proponents of this doctrine, it tends to fatalism. In fact, it is difficult to escape fatalistic conclusions if one equates foreknowledge with foreordination and believes them both. Most who have escaped it have done so by exercising the human ability to hold on to two contradictory ideas in one mind at the same time.
2. Others now teach that God has not foreordained all future events because He does not know all future events. Much about the future is open and unknown. This doctrine has been recently renewed and is called the open view of God. It teaches that the future is open to many possibilities—even in the mind of God. This doctrine limits the greatness of God and is an attack on His person as the absolute God. This is a dangerous doctrine because the very integrity of God is based on His perfect foreknowledge (Deuteronomy 18:18-22 [18] I will raise them up a Prophet from among their brethren, like unto thee, and will put my words in his mouth; and he shall speak unto them all that I shall command him. [19] And it shall come to pass, that whosoever will not hearken unto my words which he shall speak in my name, I will require it of him. [20] But the prophet, which shall presume to speak a word in my name, which I have not commanded him to speak, or that shall speak in the name of other gods, even that prophet shall die. [21] And if thou say in thine heart, How shall we know the word which the LORD hath not spoken? [22] When a prophet speaketh in the name of the LORD, if the thing follow not, nor come to pass, that is the thing which the LORD hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him.
   See All...; Isaiah 41:21-23 [21] Produce your cause, saith the LORD; bring forth your strong reasons, saith the King of Jacob. [22] Let them bring them forth, and shew us what shall happen: let them shew the former things, what they be, that we may consider them, and know the latter end of them; or declare us things for to come. [23] Shew the things that are to come hereafter, that we may know that ye are gods: yea, do good, or do evil, that we may be dismayed, and behold it together.
   See All...).
3. Finally, others as myself teach that God foreknows all future events but has not foreordained all future events. This view accepts that there are many things foreordained by God, but rejects that all things are predetermined by the will of God. Foreknowledge and foreordination are not the same in this view.

I believe that one of the problems we have with distinguishing between foreknowledge and foreordination is our inability to grasp the mind of God- and this is not going to change. According to Isaiah 57:15For thus saith the high and lofty One that inhabiteth eternity, whose name is Holy; I dwell in the high and holy place, with him also that is of a contrite and humble spirit, to revive the spirit of the humble, and to revive the heart of the contrite ones.
See All..., God inhabits eternity. That is, He dwells outside of and above time in an eternal state. Now, I cannot understand this but only accept it as true biblical teaching. However, we also know that God works in history; He deals with us in time. So, He inhabits eternity on one hand and consecutively deals with His creation in time. I cannot fully grasp this because these thoughts are too high for me.

Therefore, God sees all of the events of history (past, present, and future) in one full sweep (Deuteronomy 31:20-21 [20] For when I shall have brought them into the land which I sware unto their fathers, that floweth with milk and honey; and they shall have eaten and filled themselves, and waxen fat; then will they turn unto other gods, and serve them, and provoke me, and break my covenant. [21] And it shall come to pass, when many evils and troubles are befallen them, that this song shall testify against them as a witness; for it shall not be forgotten out of the mouths of their seed: for I know their imagination which they go about, even now, before I have brought them into the land which I sware.
See All...; Isaiah 46:9-10 [9] Remember the former things of old: for I am God, and there is none else; I am God, and there is none like me, [10] Declaring the end from the beginning, and from ancient times the things that are not yet done, saying, My counsel shall stand, and I will do all my pleasure:
See All...; Acts 15:18Known unto God are all his works from the beginning of the world.
See All...).Yet, He allows man to make many decisions on his own. Man has a free will to make his own decisions. Now just one aside: man does not have a totally uninhibited free will. I cannot will myself to be President of the United States. No person can will themselves to be a yard taller than they are. Our will is fallen and often fails us. To will is present, but how to perform is not there (Romans 7:18For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
See All...). Some have taken free will far beyond its biblical proportions and have fallen into their own errors.

My answer to the problem is that foreknowledge is not the same as foreordination or predestination (Romans 8:29For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren.
See All...; 1 Peter 1:2Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.
See All...). Foreknowledge is not of itself causative. That is, to know a future action is not the same as causing that future action to happen. Therefore, foreknowledge is not to be confused with the predetermined will of God. God does have a predetermined will, but it does not determine every action of created beings. 

Let me illustrate. I have a level of foreknowledge. It is extremely limited and sometimes faulty. However, it is the closest I can came to the real thing and it will have to do for purposes of illustration. What I mean is this: there are times when I know what someone is going to do. I mean I know it and I am seldom wrong when I know it. It is true that I base my foreknowledge on past knowledge of this person's actions. But it is still knowledge of what someone will do before they do it. I am sure you have the same experience on occasion. We know the ways of a wife, a child, or a friend to such an extent that we know what they will do in many cases. We know before they make their own decision and on occasion we know before they know what they will do. 

Now, let me ask you, does our foreknowledge of their decision in any way affect the decision they make? Has our foreknowledge removed their free will? I think not. To know what decision someone will make is not the same as forcing them to make that decision. From His eternal vantage point, God knows what we are going to do and what will happen to us in full. Some of these things He may even directly cause to happen. However, as He works in time, He can also allow us the freedom to make our own decisions in many cases (though He knows what decision we will make). That does not require a fatalistic control of all things in the universe. John, from our earlier illustration, freely choose B as God from His eternal view knew he would do. 

God's ability to work in time while knowing all is truly beyond our comprehension. Yet the Bible has examples of just this trait in God. In Genesis 49:10The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be.
See All..., Jacob prophesies of the tribe of Judah, "The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come." That is, the ruling line of Israel that will lead to the Messiah (Shiloh) will be through Judah. David was of the line of Judah, but King Saul was of Benjamin. Evidently, Saul is an aberration in the royal line, possibly caused by the impatience of Israel to have a king. 

But God has Samuel to say a strange thing to Saul in 1 Samuel 13:13-14 [13] And Samuel said to Saul, Thou hast done foolishly: thou hast not kept the commandment of the LORD thy God, which he commanded thee: for now would the LORD have established thy kingdom upon Israel for ever. [14] But now thy kingdom shall not continue: the LORD hath sought him a man after his own heart, and the LORD hath commanded him to be captain over his people, because thou hast not kept that which the LORD commanded thee.
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"Thou hast done foolishly: thou hast not kept the commandment of the LORD thy God, which he commanded thee: for now would the LORD have established thy kingdom upon Israel for ever. But now thy kingdom shall not continue: the LORD hath sought him a man after his own heart."

Do you see what he said? God would have established Saul's kingdom upon Israel forever. How could God say this when He knew that Saul would be and had to be replaced by a man from the tribe of Judah? I believe that God has an ability to act in time even though He knows all future things in perfection. He does this in a way that we cannot understand. It simply comes down to accepting everything God says about Himself without altering what we do not understand.

I truly hope that you can get some peace about this puzzle. God does not want us to simply be puzzled. He wants us to believe all that He says. May the Lord bless you in your search for His truth.