Okay. Might just be dust, but probably silicone spray residue. Yes, you can clean it if you want. It is ground plastic dust. This is common especially with new or unlubricated cubes. Take it part and wash the pieces in soapy water, lube and reassemble. It will be a lot smoother. Dec 6, 2021 · The Rubik’s cube is manufactured by melting and molding together plastic pellets to form the components and the structure of the cube. The parts are then inspected by hand to ensure they were formed properly. From there the Rubik’s cube components enter into an assembly line where the construction process is completed, the cubelet stickers ... Rubik's cube is a toy puzzle designed by Erno Rubik during the mid-1970s. It is a cube-shaped device made up of smaller cube pieces with six faces having differing colors. The primary method of manufacture involves injection molding of the various component pieces, then subsequent assembly, labeling, and packaging. Erno Rubik, who devised one of the world’s most popular and enduring puzzles, opens up about his creation in his new book, “Cubed.”. 140. Erno Rubik, who invented the Rubik’s Cube, wrote ...The Rubik’s cube is manufactured by melting and molding together plastic pellets to form the components and the structure of the cube. The parts are then inspected by hand to ensure they were formed properly. From there the Rubik’s cube components enter into an assembly line where the construction process is completed, the cubelet stickers ...Use code TINGMAN for a discount off every order at Daily Puzzles!http://dailypuzzles.com.au/tingmanAlgorithm: U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R ...May 12, 2023 · Bake accordingly in a loaf pan until top springs back. Flip the loaf onto a wire rack to cool.Turn upright to cool completely.With the cookie cutter in hand measure for the width of each slice.Cut each slice about 1″ thick..Using the cookie cutter, cut out the hearts or another shape. The movie shows him downloading files onto an SD card and then hiding it inside a Rubik’s cube. He then avoids running the Rubik’s cube through security by tossing it to a security guard, who ...3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ...REDDIT https://www.reddit.com/r/dopeornopesubmissionsHigh Steaks https://www.youtube.com/watch?v=_ZUr3kaz5wIIT'S PUZZLE TIME. Today we are looking throug...Step 1: Basics. before trying tricks I would recommend learning to solve a Rubik's Cube first . that way you know the vocabulary , tips comma and tricks . For the basic you can check out my Rubik's Cube basics instructable. Therefore we cannot solve the 5x5x5 cube. This is correct, but as the OP says that the centre caps are removable, it can be made solvable fairly easily. Just shift a middle layer one quarter turn, and rearrange that layer's centre caps to match the corners (i.e. arrange them as if to undo that quarter turn).Inside Rubik's Cube And Beyond| C Bandelow. I Choose You 2. Learning outcomes. 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars. Be a mother to my children. The Nervous Housewife. By Shore and Sedge. Shared By Two (Seeding Eden 2) by Aya Morningstar.Ever wonder what a Rubik's Cube looks like on the inside? In this video we'll take an in-depth look to see how the pieces fit together.Get your Rubik's cube...Feb 24, 2021 · February 24, 2021 9:52am. Netflix. Sue Kim, director of an Oscar-shortlisted short documentary about competitive Rubik’s Cubers, can solve a complex storytelling puzzle in under 40 minutes. In ... Inside Rubik's cube and beyond Bookreader Item Preview ... Rubik's Cube, Mathematical models, Group theory Publisher Boston : Birkhäuser Collection ture inside is the key to the Rubik ... Solving Rubiks Cube Using Open CV. Article. Jun 2022; Sudhan M.B; The Rubik’s cube is 3D combinatorial and mechanical puzzle invented in 1974. It ...We cut open, smashed open and pulled open 4 different Rubik’s Cubes to see what they are made of! This was really fun and interesting. Thank you to our many ... Play with the 3D Rubik's Cube simulator online. Press the scramble button and try to figure out the solution and practice. Use your keyboard: the buttons on your keyboard are assigned to each face, according to the notation. Face: F R U B L D. Slice: M E S. Whole: X Y Z. Uppercase letters do clockwise, while lowercase keys make inverse rotations.Erno Rubik, who devised one of the world’s most popular and enduring puzzles, opens up about his creation in his new book, “Cubed.”. 140. Erno Rubik, who invented the Rubik’s Cube, wrote ...A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. Creative Commons/Wikivisual The immediate math to be done with those numbers is the total number of ways you can scramble a...Bounds on Solving a Rubik’s Cube The number of possible permutations of the squares on a Rubik’s cube seems daunting. There are 8 corner pieces that can be arranged in 8! ways, each of which can be arranged in 3 orientations, giving 38 possibilities for each permutation of the corner pieces. There are 12 edge pieces which can be arranged in ... Sep 3, 2019 · Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/... Sep 3, 2019 · Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/... The 1x1x1 has a fairly complex notation due to its reliance on rotations to solve, so make sure you read each a few times through to ensure understanding: x – Rotates the entire puzzle by bringing the top face to the front. x’ – Rotates the entire puzzle by bringing the top face to the back. y – Brings the face on the right to the front.The 1x1x1 has a fairly complex notation due to its reliance on rotations to solve, so make sure you read each a few times through to ensure understanding: x – Rotates the entire puzzle by bringing the top face to the front. x’ – Rotates the entire puzzle by bringing the top face to the back. y – Brings the face on the right to the front.Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ...# Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :DIt's Gmod TTT! In Garry's Mod TTT today, we're inside a Rubik's cube. TTT SHIRT: https://yogsca.st/LewisTTT Gmod Playlist: https://www.youtube.com/watch?v=...Start with a Solved Rubik's Cube. Make sure all faces have the right color, and then hold the cube with the RED side facing you and the GREEN side on top. 2. Move the front side once clockwise (left to right). The front side is the RED side facing you. 3. Move the left side once clockwise (towards you).Douglas Hofstadter wrote an excellent introduction to the Rubik’s cube in the March 1981 issue of Scienti c American. There are several books about the Rubik’s cube; my favorite is Inside Rubik’s Cube and Beyond by Christoph Bandelow. David Singmaster, who developed much of the usual notation for the Rubik’s cube, This video tutorial will teach you how to disassemble and reassemble 2x2 Rubik's Cube puzzles. See the process of the 2x2 Rubiks Cube disassembly and reassembly, which is very handy for the ever-necessary lubing (especially for speedsolving), curiosity and cheating (cheating is not recommended). There are three different 2x2 puzzles that you ...Aug 24, 2014 · An explanation to the workings and layout of a 3x3x3 Rubik's cube Dec 29, 2020 · 4. 13x13 Power Speed Cube Puzzle. Creators have strived to develop new and harder twisty puzzles as a version of the original Rubik’s Cube. The most common type of the Rubik’s Cube is like the 3x3 but bigger. They can be 13x13 or N x N, also known as ‘Reduction’ or ‘Redux’. Product Information. On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in ...A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. Creative Commons/Wikivisual The immediate math to be done with those numbers is the total number of ways you can scramble a...Sep 3, 2019 · Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/... Sep 16, 2016 · The movie shows him downloading files onto an SD card and then hiding it inside a Rubik’s cube. He then avoids running the Rubik’s cube through security by tossing it to a security guard, who ... Inside Rubik’s Cube and Beyond. 1st Edition. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in ...Bounds on Solving a Rubik’s Cube The number of possible permutations of the squares on a Rubik’s cube seems daunting. There are 8 corner pieces that can be arranged in 8! ways, each of which can be arranged in 3 orientations, giving 38 possibilities for each permutation of the corner pieces. There are 12 edge pieces which can be arranged in ... Sep 1, 2023 · WHAT IS INSIDE RUBIK CUBEYour queries-cuberubiks cuberubik's cubewhat is inside rubik's cubewhat is inside speed cuberubix cuberubikrubic cuberubixwhat's ins... Rubik's cube is a toy puzzle designed by Erno Rubik during the mid-1970s. It is a cube-shaped device made up of smaller cube pieces with six faces having differing colors. The primary method of manufacture involves injection molding of the various component pieces, then subsequent assembly, labeling, and packaging. how to make a cube in a cube in a cube on the rubiks cubeThis is a very easy Cue in a cube in a cube pattern. Rubiks cube patterns are very easy and fun to m...Mar 21, 2019 · The 2x2 Rubik's Cube has an interesting mechanism on the inside. Let's see how it works!Get your 2x2 Rubik's Cube here: https://amzn.to/2ULwsqXOther puzzles... Online Rubik's Cube, 4x4x4 and other NxNxN cube solver and simulator. Set up a scramble to find the rotations leading to the solutionLocated right next to the Mad Hatter, Rubik's Arcade Bar has been one of the top places to go for nerds in El Paso; plenty of arcade machines & games to play while you can enjoy a drink too. They've hosted many trivia & karaoke events too. The place is a giant throwback to the 80s both inside & out. For the longest time, however, Rubik's was ...The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time! what is inside rubik cubeyour queries -rubiks cubecuberubik's cubewhat is inside rubik's cuberubik'srubik's cube (invention)rubikwhat is inside speed cuberub...Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/...Inside Rubik's cube and beyond Bookreader Item Preview ... Rubik's Cube, Mathematical models, Group theory Publisher Boston : Birkhäuser CollectionEver wonder what a Rubik's Cube looks like on the inside? In this video we'll take an in-depth look to see how the pieces fit together.Get your Rubik's cube...We cut open, smashed open and pulled open 4 different Rubik’s Cubes to see what they are made of! This was really fun and interesting. Thank you to our many ... The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters ( F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters ( f b u d l r) refer to the inner portions of the cube (called slices).Jun 25, 2021 · GAN 11 M PRO 3X3 👉 https://bit.ly/2SzkcOrUsing the promo code "CUBASTIC" and get your discount 🔥 The easiest way to solve a 3x3 rubik's cube 👉 https://yo... On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic.Nov 6, 2022 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ... The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters ( F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters ( f b u d l r) refer to the inner portions of the cube (called slices).Jul 13, 2020 · The Mathematical Mystery Behind Rubik’s Cube. Forty-three quintillion. Or more precisely, 43,252,003,274,489,856,000. This impressive figure is the number of tile combinations possible in the Rubik’s Cube (also known as the Magic Cube), the most famous puzzle of all times. Bearing this data point in mind, it is not surprising that the goal ... Play with the 3D Rubik's Cube simulator online. Press the scramble button and try to figure out the solution and practice. Use your keyboard: the buttons on your keyboard are assigned to each face, according to the notation. Face: F R U B L D. Slice: M E S. Whole: X Y Z. Uppercase letters do clockwise, while lowercase keys make inverse rotations.From GAN13 onFull Magnet Force. The first GAN cube to completely fill its internal space with 88 magnets. The performance of ECP 3.0 will outperform the single-line magnetic positioning systems. 8 Core Magnets. 12 Repulsion Magnets. 56 Attraction Magnets. 12 Repulsion Rings. Enhanced Core Positioning 3.0.Erno Rubik, who devised one of the world’s most popular and enduring puzzles, opens up about his creation in his new book, “Cubed.”. 140. Erno Rubik, who invented the Rubik’s Cube, wrote ...The microfluidic cube is adapted from Rubik’s original design. The cube has a total of 27 plastic components: 12 edge blocks, 8 corner blocks, 6 central blocks, and 1 cube core. The cube blocks ...Inside Rubik’s Cube and Beyond Authors: Christoph Bandelow 0; Christoph Bandelow. Bochum-Stiepel, Federal Republic of Germany. View author publications ... Aug 26, 2015 · 3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ... Feb 12, 2022 · This Rubik's cube is the easiest and the hardest at the same time. It's 1x1 and the fun part about it is that it's always in the solved state. It seems prett... The best overall performer in our testing, the GAN 11 M Pro is a pleasure to use. We loved its smooth feel, ample adjustments, and satisfyingly snappy core and corner magnets. Its relatively high ...Sep 1, 2023 · WHAT IS INSIDE RUBIK CUBEYour queries-cuberubiks cuberubik's cubewhat is inside rubik's cubewhat is inside speed cuberubix cuberubikrubic cuberubixwhat's ins... GAN 11 M PRO 3X3 👉 https://bit.ly/2SzkcOrUsing the promo code "CUBASTIC" and get your discount 🔥 The easiest way to solve a 3x3 rubik's cube 👉 https://yo...Jun 23, 2022 · Use code TINGMAN for a discount off every order at Daily Puzzles!http://dailypuzzles.com.au/tingmanAlgorithm: U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R ... A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (3 8 8!) (2 12 12!)/12. Here’s how that comes together.Ever wonder what a Rubik's Cube looks like on the inside? In this video we'll take an in-depth look to see how the pieces fit together. Get your Rubik's cube here: https://goo.gl/BEo1W5 Made with Blender 2.73 Music: "Plain Truth" by Gunar Olsen (youtube audio library) #rubiks #rubikscube #b3d1. Familiarize yourself with the Rubik's Cube. Recognize where each of the colors lie on the completed cube. [1] Notice (going clockwise) the Red, White, and Blue faces of the cube are on one side and the Green, Orange, and Yellow faces are on another. This is the standard setup for newer, standard cubes.Dec 16, 2019 · A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (3 8 8!) (2 12 12!)/12. Here’s how that comes together. A couple of my friends had the same problem. They have Guhongs, one used jig-a-loo and the white residue started appearing the next day. The other never lubricated his cube and it still formed. I don't have what you're describing, but on my Zhanchi, a little bit of oily residue collects in the cracks between the two halves of the edge pieces. A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (3 8 8!) (2 12 12!)/12. Here’s how that comes together.Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ... Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ... The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time!It's Gmod TTT! In Garry's Mod TTT today, we're inside a Rubik's cube. TTT SHIRT: https://yogsca.st/LewisTTT Gmod Playlist: https://www.youtube.com/watch?v=...The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time!View your 2x2 Rubik’s Cube from the top. Orient your cube so the white face you solved is at the bottom. Check for all the yellow corner pieces remaining. [4] 2. If you only see 1 yellow corner on the top face, use 1 algorithm. Use (R U2) (R’ U’R’ U’R’) if you see 1 yellow piece in the right hand corner.A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. Creative Commons/Wikivisual The immediate math to be done with those numbers is the total number of ways you can scramble a...From GAN13 onFull Magnet Force. The first GAN cube to completely fill its internal space with 88 magnets. The performance of ECP 3.0 will outperform the single-line magnetic positioning systems. 8 Core Magnets. 12 Repulsion Magnets. 56 Attraction Magnets. 12 Repulsion Rings. Enhanced Core Positioning 3.0.
THE ORIGINAL RUBIK’S CUBE: A combination of mathematics, art and science - the iconic Rubik’s Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980.. Local free stuff craigslist
# Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :D3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ...1. Familiarize yourself with the Rubik's Cube. Recognize where each of the colors lie on the completed cube. [1] Notice (going clockwise) the Red, White, and Blue faces of the cube are on one side and the Green, Orange, and Yellow faces are on another. This is the standard setup for newer, standard cubes.3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ...About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...2. Solving the tips and centers. The solution of the Pyraminx begins with turning the 4 corners ( A) to match the center pieces. Tthis is just a simple turn for each corner because the three sides of the center pieces ( B) are linked together. When the tips are OK, deep turn the puzzle to make the three center colors match on all faces.Jul 18, 2020 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ... From GAN13 onFull Magnet Force. The first GAN cube to completely fill its internal space with 88 magnets. The performance of ECP 3.0 will outperform the single-line magnetic positioning systems. 8 Core Magnets. 12 Repulsion Magnets. 56 Attraction Magnets. 12 Repulsion Rings. Enhanced Core Positioning 3.0.The movie shows him downloading files onto an SD card and then hiding it inside a Rubik’s cube. He then avoids running the Rubik’s cube through security by tossing it to a security guard, who ...1. White cross 2. White corners 3. Second layer 4. Yellow cross 5. Yellow edges 6. Yellow corners 7. Orient yellow corners Video tutorial To get started I recommend you to read the basic cubing terminology and you will need to know the Rubik's Cube notation ie what the letters mean in the algorithms: F: front, R: right, U: up, L: left, D: down.Mar 12, 2019 · The patent approval finally came in early 1977 and the first Cubes appeared at the end of 1977. By this time, Erno Rubik was married. Two other people applied for similar patents at about the same time as Rubik. Terutoshi Ishige applied a year after Rubik, for a Japanese patent on a very similar cube. An American, Larry Nichols, patented a cube ... A couple of my friends had the same problem. They have Guhongs, one used jig-a-loo and the white residue started appearing the next day. The other never lubricated his cube and it still formed. I don't have what you're describing, but on my Zhanchi, a little bit of oily residue collects in the cracks between the two halves of the edge pieces.GAN 11 M PRO 3X3 👉 https://bit.ly/2SzkcOrUsing the promo code "CUBASTIC" and get your discount 🔥 The easiest way to solve a 3x3 rubik's cube 👉 https://yo...Update: New and improved version. Faster, better, and supports more devices. Solving the Rubik's Mini Cube (2x2x2) may sometimes seem like an easy task comparing to solving its predecessor the original Rubik's Cube (3x3x3), however it can still pose a decent challenge for most of us - especially when trying to solve it in the shortest possible way.# Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :DThis video shows the process of taking apart and reassembling the 1x1 Rubik's Cube. Very handy for lubricating, curiosity, & cheating!Like to learn how to ac...C. Bandelow. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France ...3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ....
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