NYT hard Sudoku 29 April 2024 is sure very hard, but the much sought for rare X wing advanced Sudoku digit pattern formed for critical breakthrough.

First solve, then verify from the solution if you need.

### NYT hard Sudoku 29 April 2024: Advanced X wing pattern provided critical breakthrough

#### Stage 1: All major breakthroughs achieved, only hidden and naked singles now left

Hidden singles R7C5 3, R6C7 3, R2C3 6, R9C2 6, R4C6 9.

**Double digit scan for [5,7] in R6 on left middle major square:** **Cycle (5,7) in the major square**. **Second Cycle (1,4,9) in R6, Cycle (2,8) also in R6.**

**Single digit lock on 7 in C5:** naked double Cycle (3,8) in R2.

**Double digit scan for [2,9] in R4, C9 on left middle major square creates Cycle (2,9) in R5.**

**X wing on 8 with lock on 8 in R3 pairing up with lock on 8 in R6 with shared columns C4, C5:** DS in R9C4 [1,4] forms **Cycle (1,4,5) in C4: critical breakthrough R1C4 2.**

All else are naked or hidden singles. The game is wide open and easy to solve.

Solution next stage.

Results shown.

#### Stage 2: No challenges any more

**Start with destroying the X wing: R6C4 8.**

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.**

**Naked single may appear in many ways.** When a row (or column) has eight cells filled up, the naked single automatically becomes the candidate for the ninth cells.

In a Cycle of 2 (three or higher numbers) cells, two digits are locked up. When one of the two is reduced by new appearance of the digit in an affecting zone (row, column or major square) the second cells of the Cycle gets the naked single.

*In essence, naked single is the only digit eligible to be placed in a specific cell (all other eight digits eliminated by their presence in affecting zones). In abstraction, hidden single is also a type of naked single, but because of its ease of use, the basic operation of finding a hidden single by row column scan, a different name is used .*

**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.**

**X wing digit pattern:**

When two single digit independent locks share both rows and column, an X wing (like a large X) is formed by the four locked digits. **Its power is:** *the pattern reduces all occurrences of the locked digit from the shared pairs of rows and columns.*

This is a truly advanced digit pattern **primarily based on the good old single digit locks** and almost always provides the critical breakthrough in the puzzle. An effective X wing is less frequently appearing than double digit scan or parallel digit scan both of which are highly useful.

An asymmetric X wing of two single digit locks sharing **just two columns, but not the rows** (or rows) will reduce the locked digit from the DSs of the column (or row).

**Example:** A single digit lock is formed in row R4 in the pair of cells R4C8, R4C9. Another second single digit lock on 1 is formed in row R9 in cells R9C8, R9C9. It is apparent that the two independent single digit locks in two rows also share the two columns R8 and R9. Already digit 1 was barred from the two rows. Now because of column sharing, digit 1 is barred (eliminated from DSs) in other cells of the two columns C8 and C9 as well. Breakthrough occurs by reduction of 1 from DS of R1C8 giving DS [7,8]. This joins with a second DS [7,8] in R1C1 and eliminates [7,8] from all cells of R1. A cascade of valid digits is the result.

### More Sudoku hard puzzles you may like to solve and learn how to solve

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**How to solve Sudoku hard puzzle games full list (includes very hard Sudoku).**

*Enjoy solving Sudoku hard.*