Solve NYT Hard Sudoku 11th April 2024 puzzle at one go with careful use of the appropriate Sudoku techniques that are not fancy and difficult to understand.

First solve then learn from the solution. The puzzle and the solution should be enjoyable by both an amateur as well as an expert.

This puzzle has 23 out of 81 cells filled with digits. It is a hard Sudoku.

### NYT Hard Sudoku 11th April 2024: Easy to Understand Solution

#### Stage 1: All breakthroughs

Naked single by DS reductions R6C2 7.

**Parallel scan for 7** on R7 R7C5 7.

**Quadruple digit scan for [2,4,7,9] on left bottom major square creates Cycle (2,4,7,9) and Cycle (1,6) in the major square.**The first crucial deadlock break.

**Naked double Cycle (3,8)** in C2 by **double digit scan for [3,8] in R5. **Another special double digit scan, it may be called naked double as well.

Hidden single R4C3 6.

**DS reduction of [5,7,8] from row DS [4,5,7,8,9] in R3C5, R3C7 creates Cycle (4,9) in R3:** Breakthrough naked single R3C6 7, Hidden single R4C9 7. Power of DS reduction.

Cycle (4,9) in R4: Naked singles R4C4 3, R4C2 8, R5C2 3.

Hidden single R5C8 8.

**Double digit scan for [1,5] in R4, C9 on right middle major square: Cycle (1,5) in the major square.** A crucial Cycle for breaking open the deadlock.

**Parallel scan for 5 on C8**: Breakthrough naked singles R6C8 5, R5C7 1, R6C4 1, R5C4 7, R5C1 5, R6C9 4.

**Major breakthroughs achieved.** Routine solution next stage.

Results shown.

#### Stage 2: Routine reductions to solution

All routine.

A hallmark of these hard Sudoku puzzle is, once critical breakthrough achieved, rest of all cells are easy that need no special Sudoku techniques.

**Most important Sudoku techniques used are:** **Quadruple digit scan in the beginning, double digit scans and parallel digit scans**, all of which follow from fundamental Sudoku rules, are not conventional and **need no special effort 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.

**Quadruple digit scan:** When four digits appear in a row (or a column) and intersecting column (or row) restrict the possible cells for the four digits in the affected major square to just four, a Cycle of the four digits scanned is formed. **Unaffected empty cells in the major square** scanned must also be exactly four, and no digit scanned must be present in the major square scanned. **This follows the same principle of double digit scan and triple digit scan.**

**Example:** Digits [2,3,4,5] appear in R3 and intersecting column C5 both interacting with the top middle major square with exactly four unaffected empty cells and none of the scanned digits present in it. The powerful scan creates **a four digit Cycle (2,3,4,5) in the four unaffected empty cells** and **a second Cycle in rest of the empty affected cells.**

Atriple digit scan or a quadruple digit scan is rareand invariably provides a major breakthrough bydrastically reducing the uncertainty in the whole puzzlegame.Double digit scans appear more frequentlyin hard Sudoku puzzles.

While solving an especially hard Sudoku puzzle, lookout should always be for multiple digit scans.

**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.

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

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

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

*Enjoy solving Sudoku hard.*