Solve easily the NYT Hard Sudoku 25 Feb 2021. Apply the powerful easier unusual unconventional Sudoku techniques based on Sudoku rules.

First solve the hard Sudoku. Then verify from from the solution if you need.

### NYT Hard Sudoku 25 Feb 2021: Apply easier unconventional Sudoku techniques

#### Stage 1: All breakthroughs

Hidden singles R6C8 2, R6C7 3, R8C8 7, R4C5 8.

**Single digit lock on 6 in R3:** hidden single R1C9 6. Hidden singles R3C9 8, R1C3 8.

**Single digit lock on 5 in C7:** Naked single R9C7 1. Naked single R1C7 7.

**Cycle (5,9) in C7** top right major square: naked single R7C9 9.

**Cycle (1,9) in C9.** Naked singles R1C4 1, R7C4 8.

Hidden single R9C2 8. Naked single R9C4 2. Hidden single R5C5 2.

**Single digit lock on 1 in C6:** hidden single R8C5 1.

**R2C3 7 by parallel digit scan for 7 on R2.**

**Naked double [3,4] in R7C2 pairs up with [3,4] in R7C6: Cycle (3,4) in R7:** naked single R7C9 5, a big breakthrough. Hidden single R9C3 5, R5C1 5.

**R7C1 6 by parallel scan for 6 on C1.**

**This is the critical breakthrough.** Rest are naked and hidden singles shown in solution later.

Results.

#### Stage 2: No problems left

Routine cell resolution. **Start with R6C3 3.**

Solution.

### Easier Unconventional 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 .*

**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.**

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

The updated list of **Solutions to level 3, level 4 and NYT hard Sudoku** puzzle games:

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

*Enjoy solving Sudoku hard.*