Solve NYT Hard Sudoku 13th April 2024 without much effort with careful discovery of the breakthrough patterns using trusted Sudoku techniques.

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 13th April 2024: Solution is not difficult

#### Stage 1: All breakthroughs gotten

Hidden singles R6C9 6, R9C8 7. Naked singles R7C9 5, R5C9 7.

Hidden single R4C5 7, R1C4 7, R3C7 7, R2C3 7.

DS [1,2,4,5] in C7 reduces to **Cycle (2,4)** by [1,5] in right bottom major square: Naked singles: R1C7 5, R4C7 1. *This has been an important breakthrough resource.*

**Cycle (3,8)** in R8 and Cycle (4,5) in C8, **Parallel scan for 6** on R4: R4C6 6.

**Cycle (1,9) in C6:** naked single R2C5 3, R1C5 6.

**Cycles (1,9), (4,5)** in C6 and (4,5) in R6.

**Double digit scan for [2,3] in R4, R5** on left middle major square: Cycle (2,3) in R6: hidden single R5C2 1, R4C1 9. Cycle (1,9) in R6. *Double digit scan Sudoku technique is a real treasure and also easy to execute.*

Naked single R5C4 8. Hidden singles R9C5 8, R8C3 1.

Naked singles: R4C3 8, R4C1 9, R3C3 4.

Difficulties taken care of. Solution will be simple.

Results shown.

#### Stage 2: Simple resolutions

Easy.

Solution shown.

### 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.

### 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.*