## How to Solve Hard Sudoku New York Times 4th March, 2021: Easy Quick Solution

How to solve hard Sudoku New York Times March 4, 2021 explains each breakthrough and how advanced Sudoku techniques are used in making the breakthroughs.

### The hard Sudoku New York Times March 4, 2021

### Step by step easy Solution to Hard Sudoku New York Times March 4, 2021

Scan for 7: 7 in R2, R3, C8 → **R1C8 7.**

Scan for 7: 7 in R8, C6 → **7 locked in R7C4, R9C4: single digit lock** → **Parallel scan for 7 on R6** → 7 in C3, C4, C6 → **R6C1 7.**

Cells affected by parallel scan for 7 are colored orange and cells affected by 7 in R6 colored red.

**7 in R6C1 by parallel scan is a breakthrough.**

Scan for 7 in bottom left 9 cell square: 7 in R8, C1, C3 → **R9C2 7.**

Scan for 2 in bottom right 9 cell square: 2 in R9, C8, C9 → **R8C7 2.**

Scan for 2 in bottom left 9 cell square: 2 in R8, R9 → **R7C1 2.**

DS [5,7,8,9] in R7: [5,7] in bottom right 9 cell square affects both R7C8, R7C9 →** Cycle (8,9) in R7C8, R7C9.**

Scan for 5 in bottom middle 9 cell square and R7: 7 in C6, DS [5,7] in R7C6 → **R7C6 5.**

**Got a hit by Cycle of (8,9) and Scan together.**

Scan for 5 in bottom left 9 cell square and C1: 5 in R7, R8 → **R9C1 5 → R8C2 9 → R8C3 1.**

More next stage.

Results shown.

**R7C4 7** as the only digit left in R7.

We'll use a **single digit lock again but this time on 3 locked in R9C7, R9C9.** **This is by cross-scan for 3 on R7, C8. Usually, you'll get a worthwhile single digit lock by cross-scan for a digit on a column and a row.**

Now scan for 3 in bottom middle 9 cell square: 3 in locked R9, and in C5, C6 → **R8C4 3.** **This is a breakthrough.**

It's **time for Cycles. **

**Cycle (6,8)** in R8C5, R8C6 → **DSA on R5C6 (6,8)** → Cycle (6,8) in R5C6, R8C6 → **R6C6 2 → R6C3 4 → R6C4 8.**

Turn attention to top middle 9 cell square. Scan for 8: 8 in R2, C4 and C6 by Cycle (6,8) → **R1C5 8.**

To preserve the Cycle we'll show more next stage.

Results till now shown below.

8 in R1C5 →** R8C5 6 → R8C6 8 → R5C6 6.**

DSA on R5C2 →**R5C2 5** only digit possible in the cell → **R5C5 7 → R4C7 7** by scan for 7 in right middle 9 cell square with 7 in R5, C8, C9.

DS [1,4,5] in central middle 9 cell square and [1,5] in R5 → **R5C4 4.**

Turn attention to C2 with 3 empty cells with DS [2,4,6] → Cycle (2,6) in R3C2, R4C2 → **R1C2 4.**

By DSA on empty cells of C3 identify Cycle (2,3,9) in R1C3, R4C3, R5C3 → **R2C3 5 → R2C5 1.**

Rest next stage.

Results shown.

With 1 in R2C5 → **R4C5 5 → R4C4 1 → R9C4 9 → R9C6 1 → R1C6 9.**

DSA on R2C4 → **R2C4 6 → R1C4 2 → R3C4 5 → R1C3 3 → R5C3 9 → R4C3 2 → R4C2 6 → R3C2 2.**

With 9 in R5C3 → **R5C7 8 → R5C1 3 → R4C1 8.**

DSA on R1C9 with DS [1,6], 1 in C9 → **R1C9 6 → R1C1 1 → R2C1 9 → R3C1 6.**

DSA on R2C8 DS [3,4], with 3 in C8 → **R2C8 4 → R2C7 3.**

With 4 in C8 → **R4C8 9 → R4C9 4 → R7C8 8 → R7C9 9 → R3C7 9 → R3C8 1 → R3C9 8 → R9C9 3 → R9C7 4 → R9C8 6.**

**END.**

Final solution shown below.

The Sudoku puzzle is a challenging hard Sudoku that needed use of advanced techniques of single digit lock and parallel scan together very early in the solution stages.

Apart from basic row column digit scan and DSA (or possible digit analysis) for a cell, the **advanced Sudoku techniques** used are,

Cycles, Single digit lock twice, and Parallel scan for a digit.

To know more details on advanced Sudoku techniques, read the **solution to Hard Sudoku New York Times 3rd March, 2021.**

If you are still reading this and you are not so experienced in solving hard Sudoku puzzles, just leave aside the solution and solve the puzzle yourself.

### Suggestion

For full enjoyment, avoid looking into any solution as well as the answer.

The joy of discoveries will then be all yours.

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