54 Puzzles Solved in January 2012

posted Feb 1, 2012, 12:45 AM by Bud Lengtat

Some with notes; some without.
40 I want to solve again in 2012; 14 I don't.

I currently have 2 puzzles I haven't solved yet.
  • Dayan Gem IV
  • Gear Pyraminx

Mosaic Cube

posted Dec 19, 2011, 1:20 PM by Bud Lengtat   [ updated Dec 17, 2012, 1:14 AM ]

(When I first got it I wrote) I fiddled around with the Mosaic Cube enough to see how to cycle 3 pieces. During my first solve attempt, it fell apart. For a week it was in pieces on the desk waiting to be put together again. One rainy weekend I reassembled it with the help of a video at MeffertsPuzzles YouTube. It was a bit dicey at the end when the guy on the video used a screwdriver! I tried but failed to do it that way, but finally figured a way to get the last piece in. After assembling it, I reviewed the 3-cycles I had figured out, then scrambled it. My first solve: Corners first, then one side. Then all the centers, which are really sort of like edges only they aren't on the edge. Then the edges. Second solve: Corners first, then one side. Then some centers. Then all the edges. Then finish the centers. I stumbled upon a 5 move 3-cycle for the centers. The same thing on a normal cube scrambles two sides pretty bad.

(December 18, 2011) It has been months since I played with the Mosaic Cube and now I have no idea how to solve it, or where the notes are. 5 move 3-cycle? No idea!

(December 19, 2011) Right after I went to bed last night it hit me. I may have made a video. Got up and looked in the Movies folder. Nope. Looked in iPhoto. Nope. But there was a photo of it partially assembled that was the key to understanding. Now I can do a pure 3-cycle of centers with EPS! And a pure 3-cycle of edges with EPS. Since each corner is one twist from solved, this pretty much covers it.

4x4x4 Octahedron

posted Sep 26, 2011, 12:57 PM by Bud Lengtat

Page added.

Revisiting the Crazy 4x4x4 II

posted Sep 18, 2011, 11:43 PM by Bud Lengtat   [ updated Sep 22, 2011, 3:46 PM ]

In adding the family of 4x4x4 puzzles to the spreadsheet and this site, I eventually had to face once again, the Crazy 4x4x4 II. As I reviewed all the notes I had written before and all the solution strategies I had worked through, I wondered how in the world I ended up with the supposedly most favored strategy.

As I have re-worked through some of the strategies, something else has come to mind, inspired at least partially by something I think rline uses in some of his 4x4x4 solves—building edge pairs and moving them out of the way using EPS.

  1. Center squares—2x2x2
  2. White and yellow "inner edges"—non-white/non-yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the outer edges just like a 3x3x3 turning only outer layers.
  5. Solve the corners using 3-cycles. If 2 need to swap at the end, you have to re-solve edges after a 90˚ twist of an outer layer to make the corners solvable. Let's try something else.
  1. Center squares—2x2x2
  2. White and yellow "inner edges"—non-white/non-yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the corners like a 3x3x3 using the Corners First Method. Nope. No good. It scrambles the pieces solved in step 2.
  5. Solve the edges like a 3x3x3 using the Corners First Method.
  6. Solve the remaining circle pieces.
  1. Center squares—2x2x2
  2. Blue, Red, Green, and Orange "inner edges"—white and yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method, only hold white and yellow on the sides, and only do half the pieces.
  3. Pair up outer edges—move two pieces together then use EPS to replace them with an unmatched pair before moving back. At the end it may be necessary to use the edge 3-cycle to get the last few pieces.
  4. Solve the corners like a 3x3x3 using 3-cycle commutators.
  5. Solve the edges like a 3x3x3.
  6. Solve the remaining circle pieces.
Wait! Although pairing up edges is kind of fun, I think it is better to just solve edge pieces one by one. This takes me back to the strategy I liked most about a year ago. The very very very appealing thing about it is that it is the same steps as solving a normal 4x4x4 cube from step 2 on. So there is not a totally new strategy to learn.
  1. Center squares—2x2x2
  2. Blue, Red, Green, and Orange "inner edges" = white and yellow "centers"—use techniques like with the white and yellow edges on the 3x3x3 Corners First Method, only hold white and yellow on the sides, and only do half the pieces.
  3. Solve the corners like a 3x3x3 or 4x4x4. Corners First works. Corners can easily be matched to inner center/edges after all X's are done. Move the 2 inner layers 90˚, make the required adjustment, and move the inner layers back.
  4. Solve the edges like a 4x4x4.
  5. Solve the remaining circle pieces.
I decided. A new page has been added.

4x4x4 Family and Parity

posted Sep 9, 2011, 8:47 PM by Bud Lengtat

When I first got a 4x4x4 Cube I think I probably started by trying to solve centers first, or layer by layer. Either way I would end up sometimes with a problem at the end that I came to know after some online research as parity. How did it show itself? Two edges needed swapped. This is impossible with a 3x3x3. I don't remember if I figured out a way to deal with it on my own, or if I picked my favorite of various solutions I found online. But then I found online a way to solve the 4x4x4 centers last and I never had parity problems as long as I stuck with it. I have tried to learn and relearn exactly what parity is and why it happens, but I haven't really fully understood because today I was thinking that with a 4x4x4 supercube, in which the center pieces each has a specific home spot, there wouldn't be a parity problem at the end of the solve. Wrong! I tried solving the supercube centers first, and when I got to the end had to swap 2 edges. Time to revisit Ryan Heise's page. Chris Hardwick explains it like this: "This is the parity that is caused by solving the centers such that the edge permutation is odd. If the scramble has the edges in an even permutation and you solve the centers in an odd number of inner face quarter turns you will cause the orientation parity. If the scramble starts with the edges in an odd permutation and you solve the centers in an even number of inner face quarter turns then you will also cause the parity.

This parity is not caused by the centers. I've seen that erroneously stated on many different sites and posts on the group. The one-edge flipped parity is caused by solving the centers such that the edge pieces are in an odd permutation." This is on his website here.

His algorithm is much shorter than the method I worked out, and fixes everything in the process, but it would be one more algorithm to learn, and I am not into learning more algorithms at this point. So I will stick with working it out the way I know, and avoid having to for the most part, by solving the centers last.

Skewb Family

posted Sep 6, 2011, 2:27 PM by Bud Lengtat

Pages have been added for the Skewb, the Tetraminx/Pyraminx, the Jing's Pyraminx, and the Vulcano. They join the Crazy Tetrahedron Standard, which is also in the Skewb Family. Yet to come: Crazy Tetrahedron Mars, which I have attempted, but not yet solved. And Crazy Tetrahedron Saturn, which I have not yet attempted.

The Truth of the Cross

posted Sep 5, 2011, 12:09 PM by Bud Lengtat   [ updated Oct 13, 2014, 2:49 PM ]

by RC Sproul
At Shepherd Group September 2, 2011 Joe M brought it up again. I think he had talked about it before. During the last few months there had been several times when I thought I should do a Bible study on the cross. I want to know what the Bible says about the cross. I want to know what the death of Jesus really accomplished. Well, like so many of the "I want to..."'s of my life, I never have gotten around to delving into the Word to discover what it actually says about the subject. But then it came up again at Shepherd Group. Cornerstone Community Church in Auburn, California has a small bookstore in their lobby, and they had one more copy of the book so I took it.

The Necessity of an Atonement.

"If it is true that the cross is of central importance to biblical Christianity, it seems that it is essential for Christians to have some understanding of its meaning in biblical terms." (5-6)

People today don't feel the need for atonement.

"The prevailing doctrine of justification today is not justification by faith alone. It's not even justification by good works or by a combination of faith and works. The prevailing notion of justification in Western culture today is justification by death. It's assumed that all one has to do to be received into the everlasting arms of God is to die." (10)

Three types of theology in church history. Augustinianism—salvation rests on God's grace alone, Semi-Pelagianism—salvation rests on human cooperation with God's grace, and Pelagianism—salvation can be achieved without God's grace—an atonement is absolutely unnecessary. (12)

Why is atonement absolutely necessary?

The Just God

Why is atonement absolutely necessary? Because of the character of God. He is holy and righteous. He can not excuse sin. He must pass judgment on it. The Judge of all the earth must do right. Therefore He must punish sinners—or provide atonement for their sin. (29)

Debtors, Enemies, and Criminals

"we have violated God's justice and earned His displeasure." (32)

How does the Bible communicate the idea of sin? Three ways. As a debt, as enmity, and as a crime. (33)

"Because God is the Author of all things, He has authority over all that He has created." (34)

The created owes the Creator perfect obedience and submission. The created has failed miserably to pay what is owed and is indebted an amount that is impossible to repay.

Enmity. "Sin can be seen as a violation of the personal relationship human beings are supposed to have with their Creator. By sinning, we communicate not love, affection, or devotion to our Creator. Instead we reject Him, and declare our hostility toward Him." (37)

Sin is a crime.

"According to Anselm, each of the three characterizations of sin that we have considered—a debt, a state of enmity, and a crime—constitutes a violation of that divine righteousness, which necessitates satisfaction. When we incur a debt by failing to meet an obligation before God, that debt must be satisfied—that is, the requirements must be met in a satisfactory way. When sin creates enmity and estrangement, the requirements to end that estrangement and bring about reconciliation must be satisfied. When we commit a crime against God, His justice must be satisfied—a payment or penalty must be given or made that satisfies the demands of divine justice, or it will be compromised. We see that at the heart of Anselm's understanding of the atonement is this concept of satisfaction." (41)

"Christ, then, is the One Who made satisfaction. By His work on the cross, He satisfied the demands of God's justice with regard to our debt, our state of enmity, and our crime. In light of the facts of God's justice and our sinfulness, it is not difficult to see the absolute necessity of the atonement." (43)

Ransomed From Above

"That brings us back to the cross, where Jesus made atonement for His people, satisfying the requirements of God's justice. As we have seen, the atonement is a multifaceted event—Jesus is shown providing surety for our debt to God, mediating the enmity between us and God, and offering Himself as a substitute to suffer God's judgment in our place. But He is also seen in the New Testament as the Redeemer, the One Who redeems His people from captivity, setting them free by offering Himself as a ransom." (53)

"Christ came and paid the ransom in order to secure the release of His people, who were held captive to sin. Christ gave this ransom voluntarily, that He might redeem us from our bondage and bring us to Himself as His beloved bride." (66)

Whenever you read about a kinsman-redeemer in the OT, think about Jesus redeeming His bride.

The Saving Substitute

Jesus "made satisfaction for our debt, our enmity with God, and our guilt. He satisfied the ransom demand for our release from captivity to sin. However, there is another significant word that is often used in descriptions of the atonement: substitution. When we looked at the biblical depiction of sin as a crime, we saw that Jesus acts as the Substitute, taking our place at the bar of God's justice." (70)

The Lamb of God.

"A Substitute has appeared in space and time, appointed by God Himself, to bear the weight and the burden of our transgressions, to make expiation for our guilt, and to propitiate the wrath of God on our behalf." (81)

Made Like His Brethren

"We have seen that the facts of God's justice and man's sinfulness combine to make an atonement absolutely necessary. We also have seen that Christ Jesus, the Son of God, the second person of the Trinity, is the One Who made satisfaction for our debt, our enmity with God, and our criminal violation of the divine law. We learned that the cross was a glorious outworking of the grace of God, by which the Father commissioned the Son to make satisfaction so that sinners might be saved with no sacrifice of God's justice. And we discovered that the Bible presents Jesus as the Redeemer, the One Who frees us from our captivity by paying a ransom for us." (83–84)

"When the Protestant Reformers talked about total depravity, they meant that sin—its power, its influence, its inclination—affects the whole person. Our bodies are fallen, our hearts are fallen, and our minds are fallen—there's no part of us that escapes the ravages of our sinful human nature. Sin affects our behavior, our thought life, and even our conversation. The whole person is fallen. That is the true extent of our sinfulness when judged by the standard and norm of God's perfection and holiness." (86–87)

"I have not loved God with all of my mind. If I loved God with all of my mind, there'd never be an impure thought in my head. But that's not the way my head works." (89)

"This justification takes place ultimately when the supreme Judge of heaven and earth says, 'You are just.' The grounds for such a declaration are in the concept of imputation. This concept is found frequently in the Scriptures, and it is central to what Jesus did on the cross. For instance, we are talking about imputation when we say that Jesus bore our sins, that He took the sins of the world on Himself. The language there is one of a quantitative act of transfer whereby the weight of guilt is taken from man and given to Christ. In other words, Christ willingly took on Himself all the blemishes on the hypothetical circle we talked about earlier in the chapter. In theological language, we say that God imputed those sins to Jesus. Therefore, God looked at Christ and saw a mass of sinfulness because all of the sins of all God's people had been transferred to the Son. Jesus then died on the cross to make satisfaction for those sins—carrying out His role as the Surety, the Mediator, the Substitute, and the Redeemer." (93–94)

"...however, there is not just one transfer, there are two. Not only is the sin of man imputed to Christ, but the righteousness of Christ is transferred to us, to our account.... Because of that, when God declares me just, He is not lying." (94–95)

"But the point of the Gospel is that imputation is real—God really laid our sins on Christ and really transferred the righteousness of Christ to us." (95–96)

"It's Christ's righteousness that makes me just. His death has taken care of my punishment and His life has taken care of my reward. So my justice is completely tied up in Christ. In Protestantism, we speak of this as the doctrine of justification by faith alone... We can't earn it. We can't deserve it. We can't merit it. We can only trust in it and cling to it." (97)

The Suffering Servant

"Surely He has borne our griefs and carried our sorrows.... He was wounded for our transgressions, He was bruised for our iniquities; The chastisement for our peace was upon Him, and by His stripes we are healed. All we like sheep have gone astray; We have turned, every one, to his own way; And the Lord has laid on Him the iniquity of us all." (From Isaiah 53, quoted and expounded on 111)

"Yet it pleased the Lord to bruise Him; He has put Him to grief. When You make His soul an offering for sin, He shall see His seed, He shall prolong His days, And the pleasure of the Lord shall prosper in His hand. He shall see the labor of His soul, and be satisfied. By His knowledge My righteous Servant shall justify many, For He shall bear their iniquities.... And He bore the sin of many, and made intercession for the transgressors." (More from Isaiah 53, quoted on 113)

"The Old Testament Scriptures clearly point to the atonement. They show that it was always God's intention that His Son should come into the earth in human form, live as a man under the Law, and die a substitutionary death for His people. The Gospels, in turn, give a faithful record of the events of the crucifixion, and the epistles of the New Testament then provide an inspired interpretation of the work of the Substitute. (117)

The Blessing and the Curse

"...if Christ was not truly forsaken by His Father during His execution, then no atonement occurred, because forsakenness was the penalty for sin that God established in the old covenant. Therefore, Christ had to receive the full measure of that penalty on the cross." (120)

"Granted, the physical agony of crucifixion is a ghastly thing. But thousands of people have died on crosses, and others have had even more painful, excruciating deaths than that. But only One received the full measure of the curse of God while on a cross. Because of that, I wonder if Jesus was even aware of the nails and the thorns. He was overwhelmed by the outer darkness. On the cross, He was in hell, totally bereft of the grace and the presence of God, utterly separated from all blessedness of the Father. He became a curse for us so that we one day will be able to see the face of God. God turned His back on His Son so that the light of His countenance will fall on us. It's no wonder Jesus screamed from the depths of His soul." (135)

"Finally, Jesus said, 'It is finished!' What was finished? His life? The pain of the nails? No. The lights had come back on; God's countenance had turned back. So Jesus could say, 'Father, into Your hands I commit my spirit.'" (135)

A Secure Faith

"In fact, Calvinism is really just a later synonym for Augustinianism.

"In any case, these five singular points of Calvinistic doctrine are often summarized by the acronym TULIP, with each letter standing for one of the five points." (140)

T Total depravity

U Unconditional election

L Limited atonement

I Irresistible grace

P Perseverance of the saints

"The design of the atonement was that Christ would go to the cross, as He Himself said, as 'a ransom for many' (Matt. 20:28b). He would lay down His life, as He said, 'for the sheep' (John 10:11b). The purpose of the atonement was to provide salvation for God's elect. Simply put, Reformed theology teaches that Jesus Christ went to the cross for the elect, and only for the elect. That, in a nutshell, is the doctrine of limited atonement." (146)

"If you are of the flock of Christ, one of His lambs, then you can know with certainty that an atonement has been made for your sins. You may wonder how you can know you're numbered among the elect. I cannot read your heart or the secrets of the Lamb's Book of Life, but Jesus said: 'My sheep hear My voice' (John 10:27a). If you want Christ's atonement to avail for you, and if you put your trust in that atonement and rely on it to reconcile you to almighty God, in a practical sense, you don't need to worry about the abstract questions of election. If you put your trust in Christ's death for your redemption and you believe on the Lord Jesus Christ, then you can be sure that the atonement was made for you. That, more than anything else, will settle for you the question of the mystery of God's election. Unless you're elect, you won't believe on Christ; you won't embrace the atonement or rest on His shed blood for your salvation. If you want it, you can have it. It is offered to you if you believe and if you trust." (151–2)

"Your salvation has been accomplished by a Savior Who is not merely a potential Savior but an actual Savior, One Who did for you what the Father determined He should do. He is your Surety, your Mediator, your Substitute, your Redeemer. He atoned for your sins on the cross. (153)

Questions and Answers

"Do you see any conflict between "decision salvation" and election?

"I think the biggest danger is that churches are filled with people who have made a profession of faith but are not in a state of grace. Justification is by the possession of faith, and anyone who possesses it is certainly called to profess it. But you don't get into the kingdom of God by raising your hand, by walking down an aisle, by praying a prayer, or by signing a card. All of these acts are good, but they're externals. Unfortunately, we tend to focus on these things. When someone makes a profession, we say, 'You're in.' We don't ask the person to examine himself or herself to see whether the faith he or she is professing is authentic faith. But it's vital that we do so, because only authentic faith will bring justification. Such faith is the gift of God. I can never provoke faith in another. I can plant a seed, and I can water the seed that has been planted, but only God the Holy Spirit can bring forth the increase." (162–3)

"When... ?

In the Greek version of the Bible, the verb 'to save' appears in every possible tense. It is said that we were saved from the foundation of the world, that we were being saved from the foundation of the world, that we are saved, that we are being saved, that we shall be saved, and so on. The point is that from the foundation of the world we were justified in the decrees of God, but that was not accomplished until the space and time work of Christ and it is not realized subjectively until we are quickened by the Holy Spirit to come to faith and appropriate the benefits that were determined and secured for us in ages past." (166)


posted Sep 4, 2011, 11:26 PM by Bud Lengtat

Last November I bought a book. Desiring God, by John Piper. I read most of it, but got sidetracked and never finished. That is the story of my life. Honestly, once upon a time when I was a young preacher boy, my pastor mentor friend told me once that I had a problem of not finishing things. Anyway, I have attempted to read it again. From the beginning. It is painfully slow going for me.

In the meantime, there are other books sitting on my desk waiting in line to be read. One on the Psalms by CS Lewis that Raymond and Breann gave me. Barely started. One Marae recently bought for me by David Platt. Not even opened yet. Another on the desk that really excites me, but I haven't read yet that Marae got me about the Grand Canyon.

Friday night Joe M recommended that I read The Truth of the Cross by RC Sproul. So I bought it at church today.

God grant me the grace to read what You want me to read when You want me to read it.

Bandage Cube & Crazy 3x3x2

posted Sep 4, 2011, 11:21 PM by Bud Lengtat   [ updated Sep 5, 2011, 2:05 AM ]

Was it yesterday or the day before you added the Bandage Cube page?

This weekend I was messing with the Crazy 3x3x2 and an idea hit me that makes the solution of corners go faster. It involves the 3-cycle for the outer corners. By adding a twist of the top in the middle, it gives much greater flexibility in which 3 pieces are cycled. Usually 2 at a time can be cycled home instead of only 1, with a minimum of setup moves.

Gear and 2x2x4 Sticker Mod pages added

posted Aug 31, 2011, 3:02 PM by Bud Lengtat

I redid the Gear Cube page. The old one is still here, although I modified it somewhat thinking I would use it. But then to keep everything consistent with the spreadsheet, it was easier to replace it. There may be a copy on my computer of the complete original page that I made on one of my CTB trips.

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