Solve Sudoku Quick and Easy. Give NYT Hard Sudoku 15th April 2024 its due care. Patiently chip out the digits by Sudoku techniques based on three rules.
First solve then learn from the solution. The puzzle and the solution should be enjoyable to you.
This puzzle has 24 out of 81 cells filled with digits. It is a hard Sudoku.
NYT Hard Sudoku 15th April 2024: Solution needed patient breakthroughs
Stage 1: Patient breakthroughs
Hidden singles R2C3 8, R6C5 6, R3C2 3, R2C5 5, R5C2 5, R9C7 5, R7C1 5.
Naked single by DS reduction R7C5 2, R8C5 7, R9C5 8, R3C5 4.
Naked single R5C7 2 by long DS reduction. Naked single R8C6 9, R9C7 1, R4C7 8, R1C7 9, Cycles (4,7) in R1, (6,9) in R2.
Cycle (1,3) in C4.
Parallel scan for 4 on R5: R5C4 4.
Hidden singles R4C4 8, R3C4 9, R2C9 4.
Single digit lock on 7 in R2C8, R3C8 creates DS [3,6] in R5C8, and Single digit lock on 6 in R7C8, R8C8 creates naked single R5C8 3. This is the critical breakthrough in the puzzle.
Rest should be hidden singles and mostly naked singles.
Solution next stage.
Results shown.
Stage 2: Routine
Hidden singles and naked singles.
Solution.
Sudoku Techniques: Based on the fundamental three Sudoku rules
Hidden single: Row column digit scan: Most basic: If a digit appears in a row and a column (or a second row) to eliminate all but one cell in the intersecting major square, the digit scanned must be placed in the single cell in the major square available for it. This is a conventional nomenclature, but basically is the simple row column scan resulting in a unique valid digit cell.
DS reductions or possible digit subset reductions: The is used nearly at every step on the way to the solution. It specifically is useful for giving naked singles or Cycles. DS reduction for breakthrough usually occurs when DS in one zone (say row) interacts with the existing common digits of a second intersecting zone (say another intersecting column) reducing the DS in the intersected cell to just 1. Example: DS [5,7,9] in Row R8 intersects with Column C8 containing [5,9] reducing DS of intersected cell to breakthrough R8C8 7.
Naked single by DS reductions: When DS reduction in a specific cell by the unique digits present in the affecting row, column and the major square leaves only one possible digit for the cell, we get a unique digit valid cell. This is conventionally called a Naked Single.
Parallel digit scan: In parallel digit scan, a single digit appears in a number of rows (or columns) eliminating the cells of an intersecting column (or row) for occupancy of the digit scanned. This may leave a single cell in the affected column (or row) for the scanned digit providing a breakthrough.
Cycle: If the same set of 2 (3, 4 or 5) digits in different combinations appear in 2 (3, 4 or 5) cells of a row (or column or a major square), no other cell of the row (or column or major square) can have these Cycled digits. Example: A Cycle of (8,9) in two cells of a row debars any other cell of the row to have the digit 8 or 9.
Single digit lock: When a single digit appears in DSs of only two cells in a row (or column), the digit is locked in this row (or column) and its cells. No other cell in the affected row (or column) can host this locked digit. Usually, a single digit lock is sought for within a major square. This debars the cells of the major square from hosting the locked digit as well. For example: if digit 4 in R4 and R6 eliminates all cells of the central middle major square for 4 except R5C4 and R5C5, we get digit 4 lock in R5 and also in central middle major square. Digit 4 cannot appear in any other cell in R5 or the major square.
Single digit locks may occur also with same digit in three consecutive cells in a major square row (or column).
Rare is the single digit lock spread over more than one major square, but these may be of great value if a pair of such single digit locks happen to share two columns and two rows resulting in more valuable breakthrough digit pattern of X wing or still more powerful chained single digit locks.
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