How Many Presents from my True Love?

On the first day of Christmas my true love gave to me a partridge in a pear tree.
On the second day of Christmas my true love gave to me two turtle doves and a partridge in a pear tree.
...
On the twelfth day of Christmas my true love gave to me twelve drummers drumming, eleven pipers piping, ten lords-a-leaping, nine ladies dancing, eight maids-a-milking, seven swans-a-swimming, six geese-a-laying, five golden rings, four calling birds, three french hens, two turtle doves and a partridge in a pear tree.

So how many presents did I receive all together?

This can be solved using the differences method, which is nicely explained by Ken Ward.

In the table below, n represents the day of Christmas (starting from 0, the day before I start receiving presents), p(n) represents the number of presents I receive on that day, P(n) represents the total number of presents received so far, δ¹ is the first difference (the difference between successive terms of P(n) — which is p(n) of course), δ² is the second difference (that between successive terms of δ¹) and δ³ is the third difference.

n	0	1	2	3	4	5	6	...
p(n)	0	1	3	6	10	15	21	...
P(n)	0	1	4	10	20	35	46	...
δ1		1	3	6	10	15	21	...
δ2			2	3	4	5	6	...
δ3				1	1	1	1	...

As the δ³ values are all the same, the equation we're after is a cubic polynomial.  That is, it's of the form:

[1]P(n) = an³ + bn² + cn + d

Now we can do some substitution.  We can see immediately that

P(0) = 0a + 0b + 0c + d = 0 ⇒ d = 0

And now, from the next three terms, we can create 3 simultaneous equations:

[2]P(1) = a + b + c = 1
[3]P(2) = 8a + 4b + 2c = 4
[4]P(3) = 27a + 9b + 3c = 10

We can eliminate c, first from [2] and [3] and then from [2] and [4] to produce:

[5]6a + 2b = 2
[6]24a + 6b = 7

From which we can deduce that (24 – 18a) = 1 ⇒ 6a = 1, or a = ¹⁄₆.

Substituting that back in [5], we find that 1 + 2b = 2 ⇒ 2b = 1, or b = ¹⁄₂.

Finally we can use [2] to determine that ¹⁄₆ + ¹⁄₂ + c = 1, or that c = ¹⁄₃.

Now we can substitute these values back in [1] and tidy up a bit:

P(n)	= 1⁄6n3 + 1⁄2n2 + 1⁄3n
	= 1⁄6n(n2 + 3n + 2)
	= 1⁄6n(n + 1)(n + 2)

So, by the 12^th day of Christmas I will have received ¹⁄₆.12(12 + 1)(12 + 2) or 2.13.14 = 364 presents. Not bad going.

Grace Reigns

Grace forgives sins through the cross, and bestows on the sinner both righteousness and eternal life.
Grace satisfies the thirsty soul and fills the hungry with good things.
Grace sanctifies sinners, shaping them into the image of Christ.
Grace perseveres even with the recalcitrant, determining to complete what it has begun.
And one day grace will destroy death and consummate the kingdom.

(John Stott, commenting on Romans 5:21.)

Satan - The Ruler

The third chapter of Warren Wiersbe's book, The Strategy of Satan, summarized.

C The Ruler

Satan is described in the Bible as a ruler.

Now is the time for judgment on this world; now the prince of this world will be driven out. (John 12:31)

We know that we are children of God, and that the whole world is under the control of the evil one. (1 John 5:19)

What was David's greatest sin? You might say, "Committing adultery with Bathsheba and then having her husband killed in battle." But David committed another sin that had even greater consequences.

Because of David's adultery, just a few people died including Uriah and the baby that was born. But because of David's other sin, 70,000 people died! When David confessed his sins of adultery and murder, he said, "I have sinned." But when he confessed this other sin, he said, "I have sinned greatly."

Satan rose up against Israel and incited David to take a census of Israel. So David said to Joab and the commanders of the troops, "Go and count the Israelites from Beersheba to Dan. Then report back to me so that I may know how many there are."

But Joab replied, "May the Lord multiply his troops a hundred times over. My lord the king, are they not all my lord’s subjects? Why does my lord want to do this? Why should he bring guilt on Israel?" 

The king’s word, however, overruled Joab; so Joab left and went throughout Israel and then came back to Jerusalem. Joab reported the number of the fighting men to David: In all Israel there were one million one hundred thousand men who could handle a sword, including four hundred and seventy thousand in Judah. But Joab did not include Levi and Benjamin in the numbering, because the king’s command was repulsive to him.

This command was also evil in the sight of God; so he punished Israel.  Then David said to God, "I have sinned greatly by doing this. Now, I beg you, take away the guilt of your servant. I have done a very foolish thing."

The Lord said to Gad, David’s seer, "Go and tell David, 'This is what the Lord says: I am giving you three options. Choose one of them for me to carry out against you.’" So Gad went to David and said to him, "This is what the Lord says: 'Take your choice: three years of famine, three months of being swept away before your enemies, with their swords overtaking you, or three days of the sword of the Lord—days of plague in the land, with the angel of the Lord ravaging every part of Israel.’ Now then, decide how I should answer the one who sent me."

David said to Gad, "I am in deep distress. Let me fall into the hands of the Lord, for his mercy is very great; but do not let me fall into the hands of men." So the Lord sent a plague on Israel, and seventy thousand men of Israel fell dead.

And God sent an angel to destroy Jerusalem. But as the angel was doing so, the Lord saw it and was grieved because of the calamity and said to the angel who was destroying the people, "Enough! Withdraw your hand." The angel of the Lord was then standing at the threshing floor of Araunah the Jebusite. David looked up and saw the angel of the Lord standing between heaven and earth, with a drawn sword in his hand extended over Jerusalem.

Then David and the elders, clothed in sackcloth, fell facedown. David said to God, "Was it not I who ordered the fighting men to be counted? I am the one who has sinned and done wrong. These are but sheep. What have they done? O Lord my God, let your hand fall upon me and my family, but do not let this plague remain on your people." 

Then the angel of the Lord ordered Gad to tell David to go up and build an altar to the Lord on the threshing floor of Araunah the Jebusite. So David went up in obedience to the word that Gad had spoken in the name of the Lord.

(1 Chronicles 21:1-19)

1 Satan's target – your will

Satan's goal is to control the will. David was not deceived; he had his eyes wide open when he rebelled against God. David was not suffering; in fact, his kingdom was in great shape. Had David been deceived or had he been suffering, we might have had reason to sympathize with his decision; but this was not the case. Satan attacked David's will directly and won.

Your will is important because it helps to determine your character. Decisions mould your character, and decisions chart the directions of your life. We may want to blame circumstances or feelings, or even other people; but this is only an excuse. It is our will that directs our life.

The Christian life is basically a matter of the will. The Holy Spirit wants to instruct our minds through his word, inspire our hearts with true holy emotions, and then strengthen our will to do the will of God. You grow and serve God by praying, "Your will be done."

A dedicated Christian prays whether he feels like it or not. He obeys the word of God regardless of his own feelings. He has a consistent Christian life and a steady ministry that is not threatened by changing circumstances or feelings.

For example, we are commanded to love one another. Christian love simply means that we treat others the way God treats us, and this is primarily a matter of the will as we try to do that with the Spirit's help.

Satan is "the ruler of this world," and you and I are rebellious aliens living in his territory. Because we are citizens of heaven, we obey heaven's laws and submit to heaven's Lord. Satan wants us to worship and serve him; he wants our will submitted to his will. What weapon does he use to tempt us?

2 Satan's weapon – pride

David was feeling important when Satan approached him with the suggestion that he number the people. The previous chapter records a number of great victories that appear to have inflated his ego and enticed him to rebel against God.

When Satan tempted Jesus in the wilderness he also tried to appeal to human pride.

Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendour. "All this I will give you," he said, "if you will bow down and worship me." (Matthew 4:8-9)

Pride glorifies man and robs God of the glory that only he deserves. It's a weapon that Satan wields with great skill. It's one of his chief weapons. Even in the church, if he can get a pastor proud of his preaching, or a church member proud of their experience and skills, then he has a foothold from which to launch an attack. Let's remember Peter's words:

All of you, clothe yourselves with humility toward one another, because, "God opposes the proud but gives grace to the humble." Humble yourselves, therefore, under God's mighty hand, that he may lift you up in due time. (1 Peter 5:5-6)

3 Satan's purpose – to make you independent of God's will

God made man to be dependent. We depend on God and even our fellow man just to stay alive.

The essence of sin is to seek to be independent of God. It is to make ourselves the Creator instead of his creatures. It is to believe Satan's lie: "You will be like God."

If Satan can get you to act and think independently of God's will, he can then control your will and control your life! You will think that you just are acting freely, which is part of Satan's deception, but actually you will be acting under orders from the ruler of this world. You will be under his control.

Whenever you or I act in disobedience to God's will, we are displaying pride. It might seem to be trivial and unimportant, but everything in our lives is important to God.

So how can we learn to be totally dependent on God?

4 Our defence – the indwelling Holy Spirit

Pride is such a strong weapon and Satan is such a strong adversary that only the stronger power of the indwelling Holy Spirit can make victory ours.

Therefore, my dear friends, as you have always obeyed—not only in my presence, but now much more in my absence—continue to work out your salvation with fear and trembling, for it is God who works in you to will and to act according to his good purpose. (Philippians 2:12-13)

Working out our salvation means to bring the Christian life to completion, to accomplish in character and conduct what God has planned for us. God has a definite plan for our lives and the challenge for us is to cooperate with him in fulfilling that plan.

Finally, remember that in the battle against Satan, the only way to conquer is to surrender – to surrender to God.

That is why Scripture says: "God opposes the proud but gives grace to the humble." Submit yourselves, then, to God. Resist the devil, and he will flee from you. (James 4:6-7)

Satan - The Destroyer

This is a summary of the second chapter of Warren Wiersbe's book, The Strategy of Satan. Again, he discusses (a) his target (b) his weapon (c) his purpose and (d) the Christian's defence.

B The Destroyer

A second way the Bible describes the devil is as the destroyer.

They had as king over them the angel of the Abyss, whose name in Hebrew is Abaddon, and in Greek, Apollyon. (Revelation 9:11) [Both Abaddon and Apollyon mean destroyer.]

Be self-controlled and alert. Your enemy the devil prowls around like a roaring lion looking for someone to devour. (1 Peter 5:8)

On another day the angels came to present themselves before the Lord, and Satan also came with them to present himself before him. And the Lord said to Satan, “Where have you come from?” Satan answered the Lord, “From roaming through the earth and going back and forth in it.” Then the Lord said to Satan, “Have you considered my servant Job? There is no one on earth like him; he is blameless and upright, a man who fears God and shuns evil. And he still maintains his integrity, though you incited me against him to ruin him without any reason.” “Skin for skin!” Satan replied. “A man will give all he has for his own life. But stretch out your hand and strike his flesh and bones, and he will surely curse you to your face.” The Lord said to Satan, “Very well, then, he is in your hands; but you must spare his life.” So Satan went out from the presence of the Lord and afflicted Job with painful sores from the soles of his feet to the top of his head. Then Job took a piece of broken pottery and scraped himself with it as he sat among the ashes. His wife said to him, “Are you still holding on to your integrity? Curse God and die!” He replied, “You are talking like a foolish woman. Shall we accept good from God, and not trouble?” In all this, Job did not sin in what he said. (Job 2:1-10)

1 Satan’s target – your body

As the serpent, Satan deceives; as a lion, he devours.

Job is the prime illustration of this kind of attack. Satan did a thorough job of attacking Job’s body and all that related to it. He lost his children, his flock, his herds and his wealth, his health. His friends sat in silence with him for a week, because they saw that he was in great agony. Even Job’s wife suggested, “Curse God and die!”

When we read the Gospels, we learn that Satan, through his demonic helpers, attacked and sought to destroy the bodies of various people. One man was made dumb (Matthew 9:32,33). A woman was bent over and disabled (Luke 13:11-17). He even attacked a child and tried to get him to destroy himself in the water or the fire (Matthew 17:14-18).

Why does Satan want to do this to Christians? Mr Wiersbe suggests several reasons:

To begin with, your body is God’s temple.

Do you not know that your body is a temple of the Holy Spirit, who is in you, whom you have received from God? You are not your own; you were bought at a price. Therefore honour God with your body. (1 Corinthians 6:19-20)

God is invisible; the world cannot see him. Jesus Christ has returned to heaven and cannot be seen. But we Christians can be seen, and it is our conduct in the body that glorifies and exalts the Lord.

Not only is your body God’s temple, but it is also God’s tool.

Romans 6 encourages us offer the parts of [our bodies] to him as instruments of righteousness. (The Greek word translated “instruments” can also be translated “tools” or “weapons”.)

God often uses the various parts of our bodies, empowered by the Spirit of God, to get his work done in this world. And Satan will try to hinder God’s work by attacking God’s worker and putting his “tools” out of commission.

So we mustn’t underestimate the importance of our bodies. We must also take care of them; if we are careless about our health and safety, we are playing right into the hands of the destroyer.

The third reason Satan attacks your body is because your body is God’s treasury or investment.

We have this treasure in jars of clay to show that this all-surpassing power is from God and not from us. (2 Corinthians 4:7)

When God saved us, he put the treasure of eternal life within our bodies. We have the very life of God within us! God didn’t give us this great treasure simply to protect it – a clay jar is not the safest place for a treasure! He gave it to us so that he might invest it through us in the lives of others. Satan can rob the world of spiritual wealth by attacking the bodies of believers.

Finally, Satan attacks your body because it is God’s testing ground.

Paul says: I do not run like a man running aimlessly; I do not fight like a man beating the air. No, I beat my body and make it my slave so that after I have preached to others, I myself will not be disqualified for the prize. (1 Corinthians 9:26-27)

Your body is important to God. We must care of our bodies and use them for God’s glory. Anything in our lives that keeps us from doing our best must be abandoned. Just as a mechanic takes good care of their tools, so the believer takes good care of the tools of his body.

2 Satan’s weapon – suffering

Satan wants to make believers suffer. Again, Job is the obvious example to consider. When Job looked around, his situation was painful. Looking within, it was even more painful. Looking up, it seemed that God had forsaken him, although Job maintained his faith in God and was honoured at the end.

It is important to note that God was always in control. Satan could not go any further than God permitted. This is a great encouragement to us: We know that whatever suffering may come in our lives, God has ordained it and is in complete control.

Bear in mind, though, that there is more than one kind of suffering in the life of the Christian. We experience natural suffering simply because we are human. Romans 8 teaches us that the whole creation is groaning because of its bondage to decay and we Christians are groaning with it.

God sometimes permits his children to suffer that he might discipline them. Our heavenly Father loves us too much to permit us to be rebels, so he disciplines us that we might conform to his will. Hebrews 12:6 tells us that the Lord disciplines those he loves, and he punishes everyone he accepts as a son.

Then, God uses suffering to test and perfect our faith. In the gospels we read how he sent the disciples across the Sea of Galilee in their boat. When the disciples got away from the land, a fierce storm arose and almost sank the ship. They were not in the storm because they disobeyed the Lord, but because they obeyed him.

So not all suffering is Satanic in origin. But there is a kind of suffering that is Satan’s weapon and that is what Job experienced. It is how we respond to this suffering that determines whether Satan can gain his purpose.

3 Satan’s purpose – to make you impatient with God’s will

The only place in the New Testament where Job is named is James 5:11: We consider blessed those who have persevered. You have heard of Job’s perseverance and have seen what the Lord finally brought about. The Lord is full of compassion and mercy.

Satan’s purpose was to try to get Job to be impatient and give up. Job did become impatient with himself and his critical friends, but he never lost his faith in God. Though he did not understand what God was doing, Job knew that he could trust God and that God would vindicate him in the end.

Patience is an important Christian virtue. Unless we have patience, we can never learn many of the truths that God wants us to learn, truths that will lead us into a deeper life and a more fruitful ministry.

Consider it pure joy, my brothers, whenever you face trials of many kinds, because you know that the testing of your faith develops perseverance. Perseverance must finish its work so that you may be mature and complete, not lacking anything. (James 1:2-4)

Faith and patience go together. If we really trust God, then we will wait on him to accomplish what he has promised.

Satan tempts us that he might bring out the worst in us, but God permits it that he might bring out the best in us. Job knew this; he was able to say [God] knows the way that I take; when he has tested me, I will come forth as gold. (Job 23:10)

4 Our defence – the imparted grace of God

We don’t know Paul’s thorn in the flesh, but whatever it was, it was enough to make him pray three times. There is nothing wrong with praying when difficulties come. God did not answer Paul’s prayer in the way he wanted, but he did meet the need. He said, My grace is sufficient for you. (2 Corinthians 12:9)

Only by the grace of God can we have the patience that we need when Satan attacks the body with suffering.

And the God of all grace, who called you to his eternal glory in Christ, after you have suffered a little while, will himself restore you and make you strong, firm and steadfast. (1 Peter 5:10)

God’s grace is God’s provision for our every need. God is able to give grace for suffering to us in the same way he did with Paul and Job.

So what should you do when Satan attacks your body with suffering and tries to make you impatient with God’s will? Warren Wiersbe suggests four things:

1. Immediately submit yourself to God. If you rebel, you will give Satan another foothold in your life. Tell God exactly how you feel, but also tell him that you love him and trust him, come what may.

2. Thank God for the trials. This does not mean you enjoy the suffering, but only that you rejoice because you are suffering in the will of God, and you know that he is in control. We can be sure that Satan hates it when believers thank God in their trials.

3. Spend time in the word of God. As it tells us in Acts 20:32, the Bible is the word of his grace. God’s gracious promises will strengthen you and you’ll find the encouragements you need each day.

4. Look for ways to glorify Christ. Remember, Satan wants to use your body to disgrace the Lord; God wants to use your body to glorify him. Patience in suffering always glorifies God.

Satan - The Deceiver

Warren Wiersbe starts his helpful book, The Strategy of Satan, by concentrating on four roles that the devil assumes, four ways in which Satan tries to attack believers.  In each of those four areas he discusses (a) his target (b) his weapon (c) his purpose and (d) the Christian's defence.  This is a summary of the first chapter.

A The Deceiver

In several passages, the Bible describes the devil as the deceiver.

He was a murderer from the beginning, not holding to the truth, for there is no truth in him.  When he lies, he speaks his native language, for he is a liar and the father of lies. (John 8:44)

The great dragon was hurled down—that ancient serpent called the devil, or Satan, who leads the whole world astray.  He was hurled to the earth, and his angels with him. (Revelation 12:9)

Now the serpent was more crafty than any of the wild animals the Lord God had made. He said to the woman, "Did God really say, 'You must not eat from any tree in the garden'?"  The woman said to the serpent, "We may eat fruit from the trees in the garden, but God did say, 'You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.'"  "You will not surely die," the serpent said to the woman. "For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil."  When the woman saw that the fruit of the tree was good for food and pleasing to the eye, and also desirable for gaining wisdom, she took some and ate it. She also gave some to her husband, who was with her, and he ate it. Then the eyes of both of them were opened, and they realized they were naked; so they sewed fig leaves together and made coverings for themselves. (Genesis 3:1-7)

1 Satan's target – your mind

When Satan wanted to lead the first man and woman into sin, he started by attacking the woman's mind.  This is made clear in 2 Corinthians: But I am afraid that just as Eve was deceived by the serpent's cunning, your minds may somehow be led astray from your sincere and pure devotion to Christ. (2 Corinthians 11:3)

Why would Satan want to attack your mind?  Because it is through your mind that God communicates with you and reveals his will to you.

Several New Testament passages emphasize the importance of the mind. For example:

So I tell you this, and insist on it in the Lord, that you must no longer live as the Gentiles do, in the futility of their thinking. They are darkened in their understanding and separated from the life of God because of the ignorance that is in them due to the hardening of their hearts. Having lost all sensitivity, they have given themselves over to sensuality so as to indulge in every kind of impurity, with a continual lust for more.  You, however, did not come to know Christ that way. Surely you heard of him and were taught in him in accordance with the truth that is in Jesus. You were taught, with regard to your former way of life, to put off your old self, which is being corrupted by its deceitful desires; to be made new in the attitude of your minds; and to put on the new self, created to be like God in true righteousness and holiness. (Ephesians 4:17-24)

Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind.  Then you will be able to test and approve what God's will is — his good, pleasing and perfect will. (Romans 12:2)

God renews our lives by renewing our minds, and he renews our minds through his truth.

This truth is the word of God.  Sanctify them in the truth; Thy word is truth. (John 17:17)

If Satan can get you to believe a lie, then he can begin to work in your life to lead you into sin.  This is why he attacks the mind, and this is why we must protect our minds from the devil's attacks.

2 Satan's weapon – lies

It is important to notice the steps Satan took in getting Eve to believe his lie.

• He questioned God's word.  Indeed, has God said ...  He did not deny that God had spoken; he simply questioned whether God had really said what Eve thought he had said.  Perhaps you misunderstood what God spoke.
• He denied God's word.  You surely shall not die!  It's a small step from questioning God's word to denying it.  Of course, neither Adam nor Eve had ever seen death.  All they had to go on was the word of God, but this was all they needed.
• He substituted his own lie.  You will be like God!  Adam and Eve were already made in the image of God, but Satan tempted them with an even greater privilege: to be like God!

How did Eve respond to Satan's approach?  We get the impression that she wasn't very sure of what God had said and so was open to Satan's suggestion that God was keeping something good back from mankind.

3 Satan's purpose – to make you ignorant of God's will

Satan attacks God's word because God's word reveals God's will.  Apart from the word of God, we have no sure understanding of the will of God.  The will of God is the expression of God's love for us.

Your word is a lamp to my feet and a light for my path. (Psalm 119:105)

God wants us to know his will and to understand it.

Be very careful, then, how you live—not as unwise but as wise, making the most of every opportunity, because the days are evil. Therefore do not be foolish, but understand what the Lord's will is. (Ephesians 5:15-17)

For the Christian, God's will is not a duty; it is a delight.  He delights to discover the will of God and then obey from the heart.

If Satan can make you ignorant of God's will, he will rob you of all the glorious blessings God has planned for your life.  You will make bad decisions, get involved in sinful activities, and build the wrong kind of life.  You will also influence others to go wrong!

4 Our defence – the inspired word of God

Only the word of God can reveal and defeat the devil's lies.  You cannot reason with Satan, nor (as Eve discovered) can you even safely converse with him.  Man's wisdom is no match for Satan's cunning.  Our only defence is the inspired word of God.  Our Lord made good use of this weapon when he was tempted by Satan in the wilderness.

If you and I are going to defeat Satan's lies, we must depend on the word of God, which presents us with several challenges:

Do we take the time to get to know God's word?  The word of God is available to us in many translations.  We have the Holy Spirit within us to teach us the truths of the word.  There is a multitude of Bible study helps available.  In local churches, there are pastors and teachers who preach and explain the word.

Do we try to memorize God's word?  Jesus didn't have a concordance with him in the wilderness!  He reached back into the books of Moses, selected Deuteronomy, and quoted three verses from that book to silence Satan.

Do we meditate on God's word? Is our attitude anything like that of the author of Psalm 119:

• How sweet are your words to my taste, sweeter than honey to my mouth! (Psalm 119:103)
• I rise before dawn and cry for help; I have put my hope in your word.  My eyes stay open through the watches of the night, that I may meditate on your promises. (Psalm 119:147-148)
• The law from your mouth is more precious to me than thousands of pieces of silver and gold. (Psalm 119:72)

Here is someone who would rather have God's word than food, sleep, or money!  He took time to meditate on the word of God and enrich his soul.  It is this kind of a Christian who is able to use the word of God to defeat Satan and his lies.

Do we use God's word?  We should aim to be so saturated with Scripture that when we face a decision or a temptation, with the help of the Holy Spirit we automatically remember the Scriptures that relate to that particular situation and know how to apply them.