NYT Hard Sudoku 12th April 2024 turned out to be especially tough. An early discovery of four separated cell Cycle paved the way to later breakthroughs.
Think and solve Sudoku like an expert, and then learn from the solution.
This puzzle has 23 out of 81 cells filled with digits. It is a hard Sudoku.
NYT Hard Sudoku 12th April 2024: Solution needs some effort
Stage 1: All breakthroughs, but with an effort
Hidden single: R6C2 7, R7C9 7.
Double digit scan for [6,9] in C7 on right bottom major square: Cycle (6,9) in R8, Cycles (1,2,8), (3,4,5) in C7: naked single R9C7 1.
Double digit scan for [7,8] in C1, C6: naked single R3C6 2, R2C6 9, R3C1 4.
Cycles (1,2,5,8) and (3,7) in R2: naked single R1C8 1 ([3,7] in top left major square and in C9 reduces [3,7] from the DS of R3 to [1,2,5,8] for the four cell Cycle) in R3.
- This is the most important resource breakthrough leading to easier breakthroughs later on.
Single digit lock on 7 in C5: hidden single R9C4 7.
Single digit lock on 2 in R1C9, R2C9: naked single R4C9 6, R8C9 9, R8C8 6.
6 in R4, C3 creates breakthrough single digit lock on 6 in C1: naked single R9C1 9, R7C5 9, R1C1 2, R1C2 9, R2C9 2.
Sometimes parallel scan gives a great breakthrough: Parallel scan for 2 on C2: R4C2 2, R4C8 3.
We have reached the stage of total meltdown next stage. Results below.
Results shown.
Stage 2: All easy except one simple double digit scan
Once a simple double digit scan needed. Rest routine.
Solution shown.
A hallmark of these hard Sudoku puzzles is, once critical breakthrough achieved, rest of the cells need no special Sudoku techniques to resolve.
Most important Sudoku techniques used are: Double digit scans in the beginning, one resulting in the four separated-digit Cycle, single digit locks and parallel digit scans. All of these are derived from basic Sudoku rules, are not conventional and need no special efforts to identify complex digit patterns.
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.
Double digit scan: Same two digits appearing in a column and an intersecting row restrict the possible cells for the two digits in the affected major square to just two. This creates a Cycle of the two digits scanned simultaneously.
The digits scanned must not be present in the major square scanned and unaffected empty cells must be exactly two for creating the breakthrough two digit Cycle.
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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