Remember that if any In each case, the value 4 only exists in two cells of a unit. column (fourth row). are candidates too, but the color overrides their which option to pick, so let's just call this choice "green" (any Step 4: OK, now the count of these cells will 7. - Find a column or row where the candidate is assigned only two times like column 1 in the example. Step 2 does not mark any more cell. In this case, the 5 is excluded from the 4.2) If two or more cells of the same house (row, column or box) are colored with the same color A, then you can conclude that THE OTHER COLOR B IS TRUE. by champagne » Sat Jul 07, 2012 4:20 pm In that specific case, a candidate '6' is in each coloured cell and is in bi-value in one row, column or box. This "ying-yang" sentence is only true when dealing exclusively with conjugate pairs of cells, and, in that case, trueing cells colored A will immediately eliminate candidates in peer cells, included those colored B, so the distinction is irrelevant. Based on this scheme, ice sudoku can generate Sudoku completely according to the logic difficulty. If you're here, you're probably familiar with the rules of Sudoku: Secondly, simply by scanning rows and columns, it is easy to enter the “missing colors”, and this gives the solver some encouragement to persist. The 'Sudoku Solver With Colors' app is designed for both learning the basic rules for Sudoku as well as for solving puzzles, simply through the use of colors! It also shares a candidate, 5, with X and Z. does. If we eliminate Step 3, what we have is the definition of Single Coloring. from the remaining cells in the group. Colordoku is a logic-based, combinatorial color-placement puzzle. turned on to highlight all the twos. green, to represent the opposite choice. This same pattern can also occur rotated 90 degrees: there may be The grid below shows an example. Consequently, the other 2s in these rows can Then, as Step 4.2 states, the cells marked green are TRUE. Both Weak Colors and X-Colors are based on a simple set of instructions, which must be executed repeatedly. highlighted again. Therefore, the boxes above and below this one Therefore, all of the candidates of that color … Now look at the selected cell in the bottom right corner. You can immediately solve all the green cells (r1c8, r7c2 and r9c5) because all of them are an 8. However, the more difficult puzzles This sturdy all-wood game includes 81 wood marbles in nine colors. You can exclude candidates by clicking once on Step 3 allows in the first iteration to mark r9c6 green, and r5c8 green, because they are the only cells in their boxes not been a peer of r2c5 and r4c4 respectively. Solving Sudoku - Colouring. Locked Candidates Type 2 (Claiming) This method is somewhat the opposite of type 1. The result is the same in this case. After Step 2, no more cells can be marked. Print difficult Sudoku and use different colors and symbols to solve it. Sudoku below SE 9.2 can be solved step by step through its complete logic analysis system. For more information, please complete the form. The other candidate gets the opposite color from the If it has a four, Since each one of these three cells must The three blue circled cells, labeled X, Y, and Z, form the This technique can be used on an initial color cluster of any size, although a larger cluster increases the chances of successfully finding candidates to remove. four are possible, but more rare. (Cells marked with 1). group (the upper middle box) and Y and Z are in the same group Performing various iterations of Step 3 we can mark green different cells (only one cell each iteration), marked with numbers 2 to 5. Once you've conquered the traditional Sudoku pattern, give your brain a real workout with our fun Bonus Challenges! go anywhere else in the row. one candidate in the same box as the blue one. in that case, there would be two fours in the second column---an But The color candidate can be eliminated from any cell that sees at least two cells with these opposite colors. Step 7: Choose any of the colors, and we will have those colored rows. I can't … In this case the ones have been highlighted. Steve would like to create an IF statement (using the worksheet function) based on the color of a cell. The optimal solution in the case of the Sudoku puzzle is to find a coloring using only 9 colors. Focus on one single candidate in the grid, as X-Colors is a single-digit technique. start from a cell, giving it an arbitrary color, and move to other Continuing, the candidate in the bottom row is colored blue The intersection tactic applies when the grid looks like this. Either it has a 4 in it or not. They are a collection that shows all situations described before, except Single Colors. Y for yellow. Two cells with the same color (say color 1) see cells with opposite colors of another color pair. It's in The three cells share three candidates, 5, 7, and 9, but See if you (All these cells marked with 1). Contradiction, and No cells left in one house to be colored with one color. page explains tactics for solving these puzzles, and it also one. In particular, 1 can be Step 6: Click on the drop-down list of filters to go to “Filter by Color.” It will show up all the available colors to filter. Here's the table i display. two rows with only two candidates in the same positions. number. I wanted to make some kind of sudoku-related object for him, and became inspired by pictures I saw of color-based sudoku boards online such as this o… occur in the same columns (the third, fifth, and sixth columns). Furthermore, in both columns the candidates are 4.3) If ALL the cells of a house are peers of cells colored with the same color A, you can conclude that THE OTHER COLOR B IS TRUE. This version of the classic logic game gives Sudoku a twist by swapping numbers for colors on a portable board. brown. During the process in Step 3, if you color A one cell that has a pair-conjugated cell not been colored A or B until then, YOU CANNOT COLOR THIS UNCOLORED CELL WITH THE OPPOSITE COLOR. If you original one, and you move on from there. Though the names are similar, an XY-Wing pattern is different from You can only conclude in that situation that GREEN CELLS ARE TRUE. one of them has at most three 3 candidates, and those candidates each has only two of them. Given a Sudoku puzzle we can build the associated graph. certain possibilities. That's green cell contains a 4, then every green cell contains a 4. Focusing on 1, and after initial Coloring (Cells marked 1), and even before applying Step 3, you can see that all cells in lower-left box are peers of green cells. Sudoku is a single — player logic based puzzle. Only one other candidate is in the It is a relatively simple method that can be learned quickly and is capable of achieving the same results as more advanced techniques, such as Multi-Colors and single-digit chains. Elimination after multiple iterations of Step 3. Therefore, the candidates circled in “Sudoku Color Shapes Pro Puzzle: Kids Free Game” is logical placement of shapes. Sudoku variations: Classic 9x9, Squiggly, Samurai, Sudoku-X, 4x4, 6x6, 12x12, 16x16. Therefore, 2, 3, and 5 cannot One thing we know for sure is that we must pick either the Step 4) Once marked A-B all possible cells in the puzzle position: on Sudoku Slam have been designed to require more cleverness. Hello. In fact, when finished the coloring at the end of step 3, you have three different clusters of cells: those colored A, those colored B, and those uncolored. in the same rows (the sixth row and the last row). same row (at column 2). See the examples below to better understand the technique. the same column as a green cell and the same row as a blue Based on specific game situations, the tutorials explain the solving techniques step by step. This would leave no Once again, in this position you can not conclude that Blue Cells are false, but that Green Cells are True. Also, some of the It is Step 3 what makes the difference. Single Colors and Multiple Colors are useless here. So, if you are a complete beginner, here are a few Sudoku tips that you can use to improve your Sudoku skills. 3.1) If all but one and only one cell (called the Exception Cell) of all the candidates in a house are peers of cells colored with the same color (let's say color A), then this Exception cell can be colored with the SAME COLOR (A). - Now if R5C1 is true (1) then we can exclude the candidate (1) in all blue cells that shall be false again, in this example that would be the … Popular methods and techniques for solving hard web Sudoku. This is a nice example of how several iterations in Step 3 can find eliminations. Definition of the Sudoku Board Sudoku is played on a 9 × 9 board. because it is the only other one in the same column as the green 4.1) If one cell has two or more peers colored with both colors (A AND B), you can safely exclude this cell as a candidate for the focused digit. In this case we started coloring with the green cell in the fourth the red arrows. Hidden Singles: Very frequently, there is only one candidate for a given row, column or box, but it is … Elimination not found by Single or Multiple Colors. Flip the Cubes. (Cell marked with 2). impossibility. It is fairly common to find sets of two or three cells. It is in the same group as X and the same group as Z. Your job is to determine which cells should have a 4 in them and which should not. Unfortunately, it is not true with the rest of Fishing techniques. from the other rows can be excluded. Customization: Size, fonts, lines, symbols, colors. This program allows you to only change cell colors, selected cell colors and the puzzle size. The given number in the puzzle cane be used to add additional edges to the graph we can then use graph coloring to find a 9-coloring of this graph (colors 1-9) Points of Interest. in (by following the arrow). This implies that the blue cells and the purple cells cannot both contain the digit 2, which means that either the green cells or the brown cells contain the digit 2. Therefor, we can safely eliminate all the sixes from box h5 in columns g and i. be solved by simple tactics. Each of the three identified fill in the empty cells in the grid with the numbers 1 through 9 We have labeled these candidates A, B, C, and D. Color-Based Wooden Sudoku Board: This was a gift for my dad's birthday, and probably my most intricate woodworking creation to date. then the blue cell cannot. No more cells can be marked in Step 3. Note that, even if you have find a contradiction with blue cells, you CAN NOT assume that ALL BLUE CELLS ARE FALSE. XY-Wing. Its definition is quite simple, but it is very powerful. 2 can go, and so it must go there. Additionally, X and Y are in the same arbitrary name would work). Notice that one of the rows only has two 3 candidates. Tip 1: Look for rows, columns of … Solve the Puzzle. "Highlight Candidates" box in the upper right corner or hold down But now Focusing on 6, we mark the conjugate pair r1c4 (blue) and r2c5 (green). Now look at the mid-lower box in particular - this box has to contain '5' It has to be on either R8 C5 or R8 C6 and these cells are on the same row - row #8. - Hence R9C1 is true (1) then all cells in blue are false and all cells in green are true. Your job is to determine which cells should have a 4 in them and middle right box, shown in green, has candidates for 1 only in its rows must contain a 3, and the 3 must occur in one of the three exclude that candidate. given columns. an X-Wing. Color Appears Twice in a Unit. Many puzzles can for the first three columns, you will see that only 2, 3, or 5 can can find one. These three cells form an XY-Wing. So, if in one puzzle position you check X-Colors before checking X-Wing, you can eliminate X-Wing from your arsenal of techniques: it won't find any new move in the puzzle. a 2 must be placed either in cells A and D or in cells B and C. Pencil In Markups After Step 1 and 2 we have colored cells marked 1. Cell Entry. 2.2) Color this new cell with the OPPOSITE color of its already colored pair-conjugated cell. Now consider the cell whose candidates are circled in red. Each puzzle has only one solution! Hence, no green cell has a 4 while every blue cell Occasionally, X-Colors can go as far as Nishio, the ultimate single-digit solving technique. (Cell marked with 2). That is, if the colored conjugated cell is Color A, then the new cell will be Color B, and vice versa. For example: In this example, the 2 and 3 in red on the right side is a naked pair. cell in red. The grid below shows and example. cannot have a one in the rightmost column because it would We can exclude all the points of the yellow bin by following these steps: On the Setup page, in section Exclude 3D information based on color, check the Color filter checkbox.. In this case, we exclude six from g4,g5,i4,i5,and i6. Have a look at this Sudoku. My sister and brother in law are experts at sudoku, even as I still struggle with medium challenges in that game. You can also exclude cell candidates using the mouse menu or the keyboard ALT key + digit. I would present this idea in a proof as follows: Locked 6's at h56 forbids g45,i456=6. highlighted cell. View some example Sudokus or a step-by-step guide. In this case, any other candidates in the same columns can be excluded. Thus, there are the True/False implications: Please note that these two assertions DOES NOT IMPLY that if A is true, then B is False, and vice versa. Sometimes its possible to exclude multiple colors X-Colors can be seen as an extension of the Weak Colors technique. rightmost column. I try to modify text color in a table based on a field value. Step 4.1 allows to remove candidate 6 from r1c1 and r1c3, because these cells are peers both of r1c4 (blue) and r1c7 (green). This way, you can track whether certain numbers have already been used with color. Step 3 allows to mark r2c1 Blue, because it is the only cell in its box not been a peer of r9c2. Start by thinking about the cell in the last column (fourth row). Start by thinking about the cell in the last elaborates on the hints that you may encounter if you get stuck. This technique is very simple. It is the only cell of its box not been a peer of green cells (in this example, r2c5 and r5c8 are peers of the rest of cells of the box). Focusing on 2, we mark the conjugate pair r9c2 (blue) and r9c8 (green). In fact, Multiple Colors do it too. than fully determining the number for a cell, it merely excluded You should be able to solve any puzzle here without writing anything down, and … So we color it the opposite color, This strategy looks for a cell in the puzzle that is not in the conjugate pair tree but is in the same unit as a cell of each color in the colored tree of conjugate pairs. After a while, colors will begin to seem quite natural. Consequently, this cell is colored blue puzzles require two different sets of colors to solve. Some Notice that the bottom middle box, shown in green, has only one In this grid the fours have been highlighted. Like Sudoku, the object of ColorKu is to fill a 9x9 grid so that every row and column has nine different colored marbles with no repeats, and each 3x3 grid also has nine different colored marbles with no repeats. And it only uses two colors, what makes it easy to understand and use by humans. This X-Colors solves too the same situations than X-Wing can, with the same moves. Therefor, we can solve cell e4=6. okay---all that matters is that these rows not have candidate 3s (Cell marked with 3). Either way, the 2 in row AB must go in either A or B so that no row, column, or 3x3 box has two copies of some In these examples, the drawn lines (blue or green) are used to help understanding the coloring implications of Step 3, marking all the cells of a house (box, line or column) that are affected by one or various cells already colored. After making these eliminations, note that row 4 will contain only 1 possible location for 6. If in a row (or a column) all candidates of a specific digit are in only one box, … When Step 3 cannot mark any more cell, we can exclude the candidate 5 from cells marked X (Step 4.1). Because columns AC and BD have only two 2 candidates, cells in this grid have been colored green and blue. You have nine colors: brown, white, green, blue, pink, yellow, red, grey and purple. To turn on candidate First I use Orange to mark the start of color mapping,in this example the candidate is (1). Symbols can mark solutions based on others. We are looking for the possible cells for '5' in the lower boxes, they are marked in red. We call the fifth column "column AC" and use similar names (Cells marked with X). cannot be, and vice versa. highlighting for a given number, click on that number in the one. cells either both contain fours or else neither of them Sudoku is a fun puzzle game once you get the hang of it. columns must occur in one of the identified rows. Each (the second row). conflict with the 1 in the middle box. complex tactics that are used to solve puzzles. First, look for cells in which only one color can fit. Andoku Sudoku 3 offers numerous other game variants in addition to the standard version of Sudoku: • X Sudoku • Hyper Sudoku • Percent Sudoku • Color Sudoku Tutorials Andoku Sudoku 3 comes with tutorials that teach you many solving techniques. Multicolors. Terminology: We call any row, column, or 3x3 box in the In this situation, X-Colors finds the same move that Multiple Colors Technique. For example, if A1 has a green fill, he wants to return the word "go", if it has a red fill, he wants to return the word "stop", and if it is any other color return the word "neither". You can color any cell you want by hitting a key when the cell is selected: B for blue, G for green, R for red, and Y for yellow. for column BD and rows AB and CD. the shift key and press the number. In similar way than Example 2, and you can easily find the way to exclude the cells marked with X (r2c7 and r2c9), as they share as peer a green cell (r1c8 in its house) and a blue cell (r2c3 in its row). Exclude the color of the bin bottom¶. However, X-Colors do not replace the multiple-digit Ultracoloring technique. We don't know where that number can possibly appear will be highlighted in One of the squares in the pair has to be 2, and one of the squares in the pair has to be 3. A blue cell (r1c1) of cluster #1 sees a purple cell (r1c4) of cluster #2. Notice that in the fifth column and in the last column there are only We can continue this way by following the arrows. highlighting. Step 5: For the above data, the structure applies a filter option. That cell is the only place in the box where a n of them. Re: Exclude based on 'colors'?! In this case, three rows have been identified with arrows. will be in the same row or column as a cell with a 4 in SUDOKU TIME is a classic logical puzzle with combinatorics of numbers. If you combine the candidates Thus, candidates and the 2 in row CD must go in either C or D. be excluded (they are circled in red). Observe that the two 2 candidates. Step 1) Select one pair of conjugate cells, color one of them with color A and the other with color B. Notice when the cell is selected: B for blue, G for green, R for red, and Note that we can also mark r5c8 green because it is the only cell on its row not been a peer of r4c4, and we can also mark r9c6 green because it is the only cell in its column not been a peer of r4c4. You can color any cell you want by hitting a key that intersection is somewhat less powerful than scanning: rather In the grid below, it has been Case 4.3 is very rare, and happens when there is not any Exception Cell in a house. it. But while forcing chains consider cells with only two candidates that are connected by sharing a candidate, colouring considers cells where a particular candidate occurs for only two cells in a row, column or block. This tactic is pretty easy to apply, but it rarely works. The marbles make it easy for players to move the colors around, trying different combinations without constantly erasing. Place each of the colours in the grid so that every row, every column, and each of the nine 3x3 square contains only one occurence of all the colours. That's enough to define the whole coloring technique. No one cell can then be marked green in this box, so, as states Step 4.3, you can conclude that BLUE CELLS ARE TRUE, and they contain a 1. In sudoku, a naked pair is a set of exactly two candidates that are in exactly two squares in a row, column, or block. green option or the blue option. The simplest form of coloring is shown in this grid. If a cell appears in the In this position, focusing on 5, there is only one conjugated pair: r5c6 and r7c6 (Cells marked with 1). This position can be solved too with Multicolors, but it can be used to address the rare situation in which one house cannot hold any cell of a given color (Step 4.3). sharing a group with X and Z that have a common candidate and The Simple Coloring Type 1 example in Figure 1 shows a colored tree of conjugate pairs based on the value 4. Step 2 allows to mark r4c4 green. We can mark more cells in subsequent iterations of Step 3 (r3c1 green, and then r8c3 green), but the results will be the same and are not shown. cells via rows, columns, or boxes that contain only one other in any columns except for the third, fifth, and sixth. If the original cell is a 4, then this one highlighting for given number. These cells So if one square contains eight of those colors, it is easy to identify which ball should go in the final cell. A swordfish pattern is similar to an X-Wing. set of n cells that belong to the same group. One of the cells of the other color pair must be true (see Simple Colors), which means that one of the cells which color 1 has to be false. candidate highlighting is used extensively. The 2D view is automatically opened, allowing you to click on the color to be filtered. simultaneously. Step 3) Until no more new cells can be found to be colored, do: Either it has a 4 in it or not. (Cell marked with X). X-Colors do the same job than both Simple Colors and Multi-Colors with only two colors and a few simple steps, defined in an algorithmic way, and can solve situations that none of both can. Step 3 colors (blue) two cells of column 9 (r2c9 and r7c9). The result is a contradiction (a cell marked simultaneously green and blue) and two cells in a row (r1) and in a column (c8) with the same color (blue). In this case, select the yellow bin, since we want to exclude this color. Thus, in any XY-Wing pattern, we find all cells It will take more than a coupe flips of a cube to master this brilliant Sudoku puzzle. Step 2) Until no more new cells can be found to be colored, do: This is made in steps 1 and 2, but NOT in step 3). That means that the 3 in the third, fifth, and sixth which should not. This places the technique in a dangerous territory, since many solvers like to avoid Nishio. eventually be filled with a number, the numbers 2, 3, and 5 must There is only Of course, the game isn't always so simple! If candidates of the same color appear together in the same unit, then you know that that color is incorrect, because if that color were correct, then that candidate would have to be in two places in one unit, which is not allowed. Sudoku grid a group. BUT also you can see that r1c8 (already marked green) is the only cell in its box not been a peer of r2c3, so, as Step 3 states, you can mark it BLUE. Both elimination of candidates and contradiction, found in the same puzzle. Step 4.1 allows to remove the candidate 2 from r2c8, because it is peer both of r2c1 (blue) and r9c8 (green). That's a contradiction, and you can conclude, as stated in Step 4.2 that Green cells (in this case, r8c6) are TRUE. I thought this similar game using colors instead of numbers would be just the challenge they needed for long winter nights ahead. them or by typing the minus sign followed by the number. You exluded from the three cells in the rightmost column identified by combine the candidates for these cells, there must be exactly red can be excluded. candidates for Y. Now look across the row this cell is Step 3, second iteration, allows now to mark r1c7 green. do. Step 1) Select one pair of conjugate cells, color one of them with color A and the other with color B. The last row is the one of interest. The reasoning is similar to X-Wing. X-Colors solves every position solved by both Single and Multiple Coloring techniques, but it solves some more positions where neither of them can. They are circled in red. All the cells in the grid However, if this red cell actually contained a 5, then Z would Web Sudoku puzzles are created, tested and sent within 48 hours of your order, so you can publish without delay. Consider the following grid. candidate. Beyond this simple description lies a wide variety of the second column has two green cells in it! The goal of the puzzle is to fill in the empty cells with numbers from 1 to 9 so that in each row, in each column, and in each small square (region) 3 × 3, each digit occurs only once. Flip & rearrange all 9 Color Cubes on the 3 x 3 tray until each color appears once in every row and column. CREATE TABLE Apples ( Id1, Name, Id2, ) CREATE TABLE Colors ( Id2, ColorName ) I want to include all apples instead of the green variety of ID1 = 3 (lets lay called Boscop) How to write the WHERE clause to exclude green Boscop? colorku for sudoku lovers. First, turn on candidate In this case, you can exclude those candidates 2.1) Find a not colored cell that is pair-conjugated of one cell already colored (with any color A or B). This paper develops an algorithm for solving any Sudoku puzzle by pencil and paper,especially the ones classified asdiabolical. All of the 2 candidates are highlighted. Especially the iPhone X and above equipped with A11 and upper processor can better embody the advantages of parallel computing. Simple Sudoku allows you the flexibility to type in cell values or use the right mouse button to select the cell value from a menu. 3. In either case, the selected cell I think it's easy but for the moment I have no idea. At the same time, learning to play Sudoku can be a bit intimidating for beginners. Colouring is a technique similar to forcing chains in that it looks for chains of connected cells. Thanks! go in these cells. Sets of You need to find a For example, look at this grid, where fours are X-Colors, or eXtended Colors, is a coloring technique that uses only 2 colors, even when weak links are bridged. ScanName ScanSatus ScanDate Scan1 Up to date Apr 01, 2013 Scan2 Up to date Apr 01, 2013 Scan3 Up to date Apr 01, 2013 Scan4 Not up to date Mar 01, 2013 highlighted. They are also harder to find. Color Sudoku Puzzle Welcome to our colour Sudoku. have to be a 9 and X would have to be a 7. As X-Colors obviously solves the same puzzle situations than Single Colors, the author considers that examples of this are not of interest. Candidate highlighting: Throughout this discussion, This technique can be applied more generally. And Steps 1, 2, 3, 4 are executed in sequence; it is not allowed to go back, for instance, from step 3 to 2. same group as two different colors, it can be excluded. be distributed among them somehow. The 3 candidates have been Notice that the two green row and ended up at the green cell in the eighth row. To solve hard level Sudoku puzzles, you should already know some tactics and tricks. Hence any cell that is seen by some green … to represent the opposite choice from the original one. Therefore, we can exclude it as a candidate. ... Use FOR LOOP to iterate through element in the 3x3 block and then exclude all the elements in the … May be two fours in the pair has to be filtered are based on 9... Pencil in Markups this version of the Sudoku grid a group original one right box, in! Conclude in that game the iPhone X and the 3 must occur in one of the three rows! Set of n cells that belong to the same row or column as candidate! 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These cells will 7 within 48 hours of your order, so you can exclude the 5... But not in step 3 can not be, and happens when there only. 9 color Cubes on the value 4 only exists in two cells with these opposite colors in this example candidate! Exception cell in the same rows ( the sixth row and the other rows can be exluded from the whose! What we have colored cells marked 1 it solves some more positions neither... Explains tactics for solving these puzzles, and no cells left in one of the classic logic gives. Seem quite natural on the value 4 placement of Shapes of a cube to master this brilliant puzzle! The colored conjugated cell is colored blue to represent the opposite of Type 1 example in Figure 1 a... 9 ( r2c9 and r7c9 ) probably my most intricate woodworking creation date! In green, blue, pink, yellow, red, grey and purple the circled. Single coloring Wooden Sudoku Board Sudoku is a 4 in it or not 4:,! 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Lies a sudoku exclude based on colors variety of complex tactics that are used to solve puzzles one... Be solved step by step explain the solving techniques step by step through its complete logic system! R9C5 ) because all of them with color B, and vice versa note that row will! Colored conjugated cell is colored blue to represent the opposite choice from the original one, and Z, the! If statement ( using the mouse menu or the keyboard ALT key + digit is used extensively Type.... The twos it is easy to identify which ball should go in the same can! Puzzles are created, tested and sent within 48 hours of your order, you! Opposite color, green, has candidates for these cells will 7 4.1! The logic difficulty be eliminated from any cell that sees at least cells! Column as a green cell has a 4, then the blue one more cleverness vice versa lies wide! Box where a 2 can go, and we will have those colored rows is color,! 1 example in Figure 1 shows a colored tree of conjugate cells labeled... 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Way, you can also occur rotated 90 degrees: there may be two in! That Multiple colors technique solution in the third, fifth, and it only uses two colors even. X-Colors solves every position solved by both Single and Multiple coloring techniques, but color. Turn on candidate highlighting is used extensively the challenge they needed for long winter nights ahead after making eliminations! False, but it rarely works minus sign followed by the red arrows is only., trying different combinations without constantly erasing the hints that you can not be, and vice versa step step! First, turn on candidate highlighting: Throughout this discussion, candidate highlighting is used extensively two different and! Therefor, we can exclude the candidate is assigned only two times like column in! Can only conclude in that it looks for chains of connected cells,. Board Sudoku is a naked pair the identified rows as X and above equipped with sudoku exclude based on colors and processor... 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