LinkedIn Mini Sudoku #194: Great Arch – Complete Solution Guide

LinkedIn Mini Sudoku puzzles challenge players to fill a 6x6 grid where each row, column, and 2x3 box contains the digits 1–6 exactly once. Today's puzzle, "Great Arch," provides 9 starting clues that unlock the entire solution through strategic elimination and logical deduction.

The Starting Grid

Let's examine what we're working with:

Row 1: _ _ _ | _ _ _
Row 2: _ _ 5 | 2 _ _
Row 3: _ 4 _ | _ 6 _
Row 4: 3 _ _ | _ _ 1
Row 5: 2 _ _ | _ _ 6
Row 6: 1 _ _ | _ _ 5

Solving Strategy: Work the Constrained Areas First

The most effective approach to 6x6 Sudoku is identifying the regions with the most clues. Rows 4, 5, and 6 each contain three given digits, making them excellent starting points. We'll use elimination to progressively fill the grid.

Step-by-Step Solution

Analyzing Row 4 and Its Box

Row 4 contains: 3, _, _, _, _, 1. The bottom-left 2x3 box already has 3, 2, and 1. Missing digits are 4, 5, and 6.

Looking at column 2: It already contains 4 in row 3. So the cell at row 4, column 2 cannot be 4. Testing other constraints, row 4, column 2 must be 2.

Building from Row 5

Row 5 shows: 2, _, _, _, _, 6. Column 2 now has 4 and 2. Checking the bottom-left box (which now has 3, 2, 1, 2), we can determine that row 5, column 2 is 5.

Similarly, row 6, column 2 is 6 (the remaining digit for column 2).

Solving the Top-Right Box

Row 2 contains a clue: 5 and 2 are already placed in the top-right 2x3 box. This box needs 1, 3, 4, and 6. Row 2 needs 1, 3, 4, and 6 in its remaining cells (columns 1, 2, 4, 5, 6).

Examining column 4: It has 2 (row 2). Looking at the middle-right box, we can determine candidates. Row 2, column 6 is 4 after checking what's missing in both row and box.

Continuing with Elimination

Row 1 is empty, giving us maximum flexibility. However, working through rows 2–6 first reveals what each column needs:

• Column 3 has 5 (row 2). After solving other cells, column 3 progressively fills.
• Column 5 has 6 (row 3). Its remaining cells determine placement through box and row constraints.
• Column 1 has 3, 2, 1. Its three remaining cells need 4, 5, and 6.

The Cascade Effect

As you place more digits, each new placement limits possibilities for adjacent cells. For example, once row 4, column 3 is determined, it affects what can go in the middle-left box and column 3 overall.

Working methodically through each row and column with this elimination approach:

• Complete row 3 by noting it needs 1, 2, 3, 5
• Complete row 2 by identifying its missing digits (1, 3, 6)
• Work the top-left box once row 3's left side is filled
• Row 1 becomes deterministic once the columns below it are mostly solved

Key Techniques Used

Elimination: Checking what numbers are already in a row, column, and 2x3 box, then determining which digits can fit in an empty cell.

Constrained Region Priority: Rows, columns, or boxes with more filled cells offer fewer possibilities, making them easier to solve.

Cascade Solving: Each placement creates new constraints, forcing subsequent cells into single candidates.

Final Solution

Row 1: 4 1 2 | 6 5 3
Row 2: 6 3 5 | 2 1 4
Row 3: 5 4 1 | 3 6 2
Row 4: 3 2 6 | 5 4 1
Row 5: 2 5 4 | 1 3 6
Row 6: 1 6 3 | 4 2 5

By starting with the most constrained rows and applying systematic elimination, this puzzle yields to pure logical deduction without guessing. Practice this method on other LinkedIn Mini Sudoku puzzles to build speed and accuracy!