To preserve the breakthrough digit patterns the stage is closed here with status shown below. Every such easy fill at this stage is a bonus. [2,6] in two cells of C3 forms a Cycle in which the two digits get locked and thus disallows appearance of 2 and 6 in any other empty cell of C3. With much of the empty cells filled up with valid digits, short length possible digits are evaluated conveniently in promising zones by possible digit analysis technique. DS in R8C2 [2,5,6] by reduction of 1 in C2 from DS [1,2,5,6] in R8 and DS in R8C3 [2,6] by reduction of [1,5] in C3 from DS [1,2,5,6] in R8. AFRAID INCOME LAGOON STYLUS AFFECT DUPLEX. As a strategy we always start row column scan from digit 1 and continue till digit 9. This will result in a series of valid cells and is a major breakthrough. Now do a parallel scan for 1 in empty cells of column C6 to get the valid cell R1C6 1. Writing long digit sets takes more time and effort. Solve New York Times Sudoku hard February 20, 2021 in quick steps. With 1 in R1C6, R3C5 2 by reduction -- R1C5 8 by reduction -- R2C6 4 by reduction -- R9C6 8 by reduction caused by the Cycle (3,9) formed in R6C6, R8C6. Bur that would have been time-taking. With 4 in R1C8, R5C8 9 by reduction -- R5C7 4 by reduction -- R3C7 9 by exception in C7 -- R3C8 9 by exception in whole game. An interesting property of a valid cell by parallel digit scan is, there will always be an associated Cycle after you put the valid digit in its identified cell. In early 2022, we proudly added Wordle to our collection. R7C1 2 by DS reduction of [1,4,6] in C1 from possible digit subset DS [1,2,4,6] in four empty cells of R7. Analyze in which cell digit 5 can appear in R2. This is a powerful way to get a valid cell. SuDoku Archive for October 2012. The NY Times Sudoku Hard 4th March 2021 solved step by step quickly and easily by advanced Sudoku techniques with breakthroughs explained adequately. With 7 in R4C3, R1C3 3 by reduction -- R1C2 7 by reduction. That's why for speed, we prefer to identify parallel digit scan possibilities. Be VERY careful about your notes. We'll select relatively more promising cells in a row, a column or a 9 cell square (each a zone) to evaluate the smallest length of possible digits in the cells first. These are rough figures drawn from experience. Solution to the New York Times Sudoku Hard, 15th February, 2021: Stage 1: Early breakthroughs by Single digit lock and parallel scan Use row-column scan, the simplest method to get a unique digit for a cell. With 6 in R6C9, R7C9 4 by reduction -- R7C7 6 by reduction and exception in C7. Breakthrough R3C3 4 by DSA reduction of [3,7,8,9] from possible digit subset of [3,4,7,8,9] -- R3C7 8 by reduction from DS [4,8] -- R1C7 4 by reduction and exception in top right major square. How debt-for-climate swaps can help solve low-income countries' fiscal and environmental challenges at the same time R2C9 2 by DSA reduction of [1,4,9] in R2 from DS [1,2,4,9] in C9. R9C7 4 by reduction of 6 from DS [4,6] from R9 -- R9C8 6 by exception in R9 -- R2C8 4 by exception in C8 -- R2C7 3 by exception in whole game. An often asked questions is, "What makes a Sudoku puzzle hard?". Alternately, if R4C3 6, digut [1,7] will appear in eithe of the cells R5C3, R6C3. To start with, R4C9 1 by DSA reduction of [4,9] in R4 from reduced DS [1,4,9] in C9 -- R8C8 1 by single digit lock partner reduction of 1 in R8C9. Step by step solution to the New York Times Sudoku Hard 20th February, 2021: Stage 1: Breakthroughs by Double digit scan, DSA technique and Cycles First success by row-column scan: R8C8 4 because of 4 in R7, R9 -- R9C9 2 by scan for 2 in R7, C7. Well not disturb the Cycle of (6,8) for better understanding of what happened at this stage. Specifically important is the disallowing of digit 5 in the empty cells of C3. To be quick select the digit that appears maximum number of times and select a promising 9 cell major square for row column scan on its empty cells. R6C1 7 results in R9C2 7 by scan for 7 in C1 -- R9C1 5 by exception in bottom left major square. This creates Cycle (7,8) in R4. For example, if we get a useful pattern and a hit after enumerating just a few cell digit possibilities, we continue exploring the hit to get further hits. Learn more about how to play The New York Times' word games and logic puzzles: Wordle, Spelling Bee, Letterboxed, Tiles, Vertex, and Sudoku. Hint #1: The word contains three vowels (madness isn't it) one of which, in a different word structure, could be a consonant. By possible digit analysis we have the DSs in R4C3, R5C3 and R6C3 as [1,6], [1,6,7] and [1,6,7]. Copyright: Atanu Chaudhuri and respective Authors. If by DSA reduction we get a single digit possible for a call, we get a valid cell hit. A single digit lock is always a valuable asset for hard Sudoku simplification and whenever yoi identify such a possibility, just note it in your mind for future use at the right timer. DS in C1 [1,2,5,7] reduced by [2,7] in R7 to form DS [1,5] in R7C1, reduced by 7 in R8 to form DS [125] in R8C1 and reduced by 2 in R9 to form DS [1,5,7] in R9C1. Copyright: Atanu Chaudhuri and respective Authors. The joy of discoveries will then all be yours. We eliminate repeated digits when considering digits of two or three zones together. The New York Times Sudoku Hard, 17th February, 2021 Before going through the solution solve the puzzle first. This prompts us to look for a valid cell caused by this single digit lock and thus discover the difficult to identify R2C5 5 by parallel digit scan for 5 on empty cells of R2. By the way, Sudoku hard solution techniques are included with many of the solutions. If you cannot logically place a value in a cell then do not place that value in a cell. Results of the actions taken shown below. Copyright: Atanu Chaudhuri and respective Authors. This NY Times Sudoku puzzle with only 23 filled cells is fairly hard and well-balanced. There is no metric or measurement to decide for sure that a Sudoku puzzle is hard, or not so hard. Next R1C8 7 by scan for 7 in R2, R3, C9 and that's all by row column scan at this point. In this case for example, after you put 5 in R2C5, a Cycle of remaining four digits [4,6,7,8] is formed. With 9 in R4C9, R4C1 8 by reduction of 9 from possible digit subset of [8,9] in C1 -- R5C1 9 by exception in C1. Nevertheless, a distinction between hard, medium and easy Sudoku categories can be made. In the new paper, Dr. Getzin and his colleagues noted that termites were conspicuously missing from their study sites, and that they found no signs of root damage in grass that died after rainfall . This is a breakthrough by single digit lock and DSA. Instead, focus has been to aggressively create a breakthrough at the earliest as well as taking the opportunity of a valid cell by the simplest technique of row column scan. This Sudoku hard is a challenging puzzle rich with Sudoku digit patterns. These puzzles are New York Times Sudoku Hard 17 February, 2021 solved in four stages that explain all breakthroughs and how those are achieved by advanced Sudoku techniques. By the way, Sudoku hard solution techniques are included with many of the solutions. Enjoy also learning how to solve Sudoku hard in easy steps. This Sudoku hard is an especially challenging puzzle rich with Sudoku digit patterns. Every such easy fill at this stage is a bonus. The . Then start the process for the next higher digit. As a ball-park figure, any Sudoku puzzle having number of filled up cells 27 and below should be taken as hard or extremely hard. Wordle players can use these five hints to solve puzzle #500. It's a pleasant surprise to identify that a Cycle of [1,2,5,6] is formed in the four cell DSs in R7C1, R8C1, R8C2 and R8C3. We can say with 100% certainty that these three digits will be placed in the final solution in only these three cells and nowhere else. If Costner's 1989 baseball movie had featured zombies, it could have been called - FIELD OF "SCREAMS" (Distributed by Tribune Content Agency) As a byproduct the leftover two digits [1,8] form a Cycle of (1,8) in R6C2 and R6C3. R4C7 7 by scan for 7 in C8, C9 -- R3C7 9 by reduction of 8 from DS [8,9] in R3 -- R3C9 8 by exception in R3 -- R7C9 9 by reduction -- R7C8 8 by reduction -- R4C9 4 by reduction of 9 from DS [4,9] in R4 -- R4C8 9 by exception -- R9C9 3 by exception in C9. You can include the QR code to any puzzle that is 9x9, for instance, to make it unique. The New York Times regularly publishes a number-based puzzle game called NYT Sudoku. Note: To know more on DSA reduction technique, click on the above internal link and return (after going through it) by clicking on browser back button. With 1 in R5C6, R3C6 9 by reduction -- R3C4 1 by exception -- R7C6 6 by reduction. Next breakthroughs by forming Cycle (8,9) in R7C, R7C9 by DSA reduction in both cases by [5,7] from possible digit subset [5,7,8,9] in four empty cells of R7. No more digits can be placed by this simple method of row-column scan at this point. But by DSA we get the valid cell, R8C2 9 by reduction of [1,5,7] from bottom left major square DS [1,5,7,9] -- R8C3 1 by reduction of [5,7] in R8 from DS [1,5,7] in bottom left major square. With this basic concept in place start row column scan for the lowest digit 1 and continue the process till a digit is finished or ends in a block of no more success. 3 Sudoku types . Because of the series of early breakthroughs by advanced digit patterns, the Sudoku hard could be solved rather easily. Nevertheless, a distinction between hard, medium and easy Sudoku categories can be made. This creates an opportunity for us to apply advanced technique of double digit scan to get a breakthrough Cycle (1,8). This breakthrough gives us two more valid cells, R3C7 8 by reduction from DS [4,8] -- R1C7 4 by reduction and exception in top right major square. For example, R5C5 2 by DSA reduction of [1,5] in the parent top middle major square itself from the possible digit DS of [1,2,5] in C5. These four digits are locked and are self-sufficient in these four cells, each appearing at least twice in these four cells. This creates an opportunity for us to apply advanced technique of double digit scan to get a valid cell hit. Because of 8 in central middle major square, R5C6 6 by reduction of 8 -- R8C6 8 by reduction of 6 -- R8C5 6 by reduction of 8. First valid cell by row column scan is for 5: R4C2 5 by scan for 5 in R5, R6. That means, these two digits light up or affect the intersecting cell R6C1 and reduce its possible digit subset to single digit 3. The joy of discoveries will then all be yours. In medium or easy Sudoku puzzles, number of filled up cells will be more. R6C9 4 by DSA reduction of [7,9] from DS [4,7,9] -- R6C7 7 by reduction -- R5C9 9 by exception in right middle major square -- R3C9 3 by exception in C9. Play the USA TODAY Sudoku Game. Before going through the solution solve the puzzle first. Still analyzing this promising neighborhood we detect the possibility of the next breakthrough of R2C1 3 by parallel scan for 3 on empty cells of C1. Set union is technical, but this we do by common sense and do naturally. You get a valid cell breakthrough in R2C5 5. Description - Self Solving Sudoku - Slice and Dice - Locked Candidates Pointing - Triple Subset - Pair - Locked Candidates Claiming - New York Times Sudoku Hard October 21, 2022 -. Identify the rows and columns with the digit that intersect in a cell in the the 9 square major square. This is the quick method of parallel scan for digit 8 on empty cells of the row R8. As a strategy we always start row column scan from digit 1 and continue till digit 9. There is no metric or measurement to decide for sure that a Sudoku puzzle is hard, or not so hard. Select a Word Game to learn more: Wordle. Enjoy also learning how to solve Sudoku hard in easy steps. Since the launch of The Crossword in 1942, The Times has captivated solvers by providing engaging word and logic games. Consider the row column cross-scan: With digit 5 in R4C2, and R7C9, 5 can appear only in two cells R8C3 and R9C3 of bottom left major square Thus the digit 5 is locked in C3 as well as in the parent major square. Description- Self Solving Sudoku- Slice and Dice- Locked Candidates Pointing- Locked Candidates Claiming- Pairs- Locked Candidates Pointing- New York Times S. So the last breakthrough has been R9C1 7 by reduction of [1,5] from DS [1,5,7] because of the Cycle (1,2,5,6) in bottom left major square. Strategy adopted: start with row column scan coupled with aggressive breakthroughs by advanced Sudoku techniques. With six digits filled in the left middle major square, it is a very promising zone to look for more valid cell hits. To be able to solve a Sudoku puzzle in a short time you should know how to use the pencil to trace the board. Because of this locked status of the digits in the cells involved in the Cycle, all occurrrences of these locked digits in zones containing the Cycle are reduced. We'll now show you a special valid cell breakthrough by a combination of advanced patterns of single digit lock and parallel scan. Cycle reduces possible digit subset for R7C4, R7C6 to [5,7] and with [7] in C6 we get the breakthrough R7C5 5 by reduction of 7 followed by R7C4 7 by exception. This is the hallmark of a truly Sudoku hard puzzle game. The updated list of Solutions to level 3, level 4 and NYTimes Sudoku hard puzzle games: How to solve Sudoku hard puzzle games full list (includes very hard Sudoku). So we'll next start evaluating 2 or 3 digit possible digit subsets DSs in . With 5 in R1C1, R3C2 2 by reduction -- R5C2 6 by reduction -- R6C3 2 by reduction -- R6C4 6 by reduction -- R5C6 1 by reduction -- R5C4 2 by reduction. This leaves the single cell R2C1 for 3 and the byproduct Cycle of (5,6,7) in the other three empty cells of C1. Next valid cell is R4C6 7 by scan for 7 in R5, R6, C7. If yes, then we have provided all the NY Times Sudoku Answers. This is a breakthrough that otherwise couldn't have been achieved. R9C8 2 by scan for 2 in C7 -- R9C3 5 by reduction -- R8C3 2 by reduction -- R9C4 4 by reduction -- R8C4 5 by reduction and exception. This makes the digit invalid in any other cell in the row or column in which the digit is locked. Play the Daily New York Times Crossword puzzle edited by Will Shortz online. Description- Self Solving Sudoku- Locked Candidates Pointing- Triple Subset- Locked Candidates Claiming- Pair- New York Times Sudoku Hard September 14, 2022-. We don't bother about other digits appearing in these two cells. In the process, an awkward shaped Cycle (1,2,5,6) in bottom left major square formed. Primarily, with only two cells left for the two digits, a breakthrough Cycle of (1,8) is formed in a single strike and it leaves only the cell R6C1 for digit 4 by exception in left middle major square. This breakthrough DS of [6,8] joins with [6,8] in R8C6 to form breakthrough Cycle [6,8] in C6 reducing DS in C6 to [1,2,9] and causing the breakthrough in R6C6 2 by reduction of [1,9] from C6 DS [1,2,9] -- R6C3 4 by reduction of [2,8] -- R6C4 8 by exception in R6 -- R1C2 4 by scan for 4 in R3, C1, C3. R4C4 4 by scan for 4 in R5, R6, C6 -- R4C6 5 by exception in R4 -- R5C5 7 by scan for 7 in C4, C6. Cycle (4,7) in R1C4, R1C6 in top middle major square and in R1 by reduction of [8,9] in R1 from possible digit subset [4,7,8,9] in top middle major square -- R1C3 5 by exception in R1 as the only cell left for 5. It can also be helpful to mark the columns and rows with pencil marks to work through elimination methods. It a Sudoku hard rich with learning potential. Do you play the New York Times Sudoku? Though number of digit 3 is small, we identify first a single digit lock for 3 in R9C7, R9C9 by cross scan for 3 in R7, C8. R2C3 5 by parallel digit scan for 5 on empty cells of C3: 5 in R1 debars R1C3 for 5, 5 in left middle major square debars R4C3, R5C3 for 5 leaving single cell R2C3 for 5 -- R2C5 1 by reduction of [5,8] from DS [1,5,8] in C5 -- R4C5 5 by reduction of 1 -- R4C4 1 by reduction and R1C5 8 by exception in C5. We stop in a 9 cell major square when the rest of the empty cells would all have digit possibilities 4, 5 or more. In easy ones it can be 36 or more. Try free NYT games like the Mini Crossword, Ken Ken, Sudoku & SET plus our new subscriber-only puzzle Spelling Bee. As a subscriber, you have 10 gift articles to give each month. Single digit lock on 4 in R2C2, R3C2 by scan for 4 in C1 -- DS in R7C2 [1,4] is reduced by 4 by the lock on 4 in C2 resulting in R7C2 1 -- R8C9 1 by scan for 1 in R7 -- R8C3 4 by scan for 4 in C1, lock on 4 in C2. Once a few cells are filled in a zone, enumerating the rest gets easier. Note: For more details, you may click on the section link on "How the parallel digit scan works" above and return by clicking on browser back button. To be precise, this is what happens in the double digit scan for [1,8] together on the empty cells of the left middle major square. By the double digit scan, first the Cycle is formed and then the valid cell R6c1 4 by reduction of [1,8] because of the property of the Cycle. How to solve the Sudoku hard is explained clearly including all the breakthroughs. R4C1 8 by reduction of 3 from DS [3,8] in C1 -- R5C1 3 by exception in C1 -- R5C7 8 by exception in R5. But when you face a Sudoku hard, valid cell by row column scan may be few or non-existent to start with. Enjoy also learning how to solve Sudoku hard in easy steps. Before going through the solution solve the puzzle first. The possible digit subset in the three empty cells is [1,4,8]. Enjoy solving Sudoku hard. After speed of solution, reducing labor being the main objective, we won't enumerate 4 or 5-digit possibilities or enumerate possible digits for ALL the cells. It is followed immediately by a second valid cell for 7 in the promising neighborhood of left middle major square: R5C2 7 by scan for 7 in R6. This eliminates the cell R6C1 for any of the two digits. Leftover three digits in C3 form a Cycle (1,6,7) in R4C3, R5C3, R6C3. The elimination of four empty cells for 5 in row R2 is shown by red arrows in the Stage 2 solution figure below. About New York Times Games.
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