Firework

Level 8 · Blue Belt

Strategy:

Firework

Overview

Firework uses a pivot cell at the intersection of a row and column, where a digit has strong links along both the row and column. The pattern forces the digit into specific cells, allowing eliminations elsewhere.

How It Works

  1. Find a pivot cell at the intersection of a row and column.
  2. The digit must form a conjugate pair in the row (pivot + one cell) and column (pivot + one cell).
  3. The digit must be in the pivot or in both endpoint cells.
  4. Eliminate the digit from cells seeing both non-pivot endpoints.

Example

Starting position

Look for Firework.

1

Firework pattern pivoting on r1c6

Found a Firework pattern. Pivot r1c6 at the intersection of Row 1 and Column 6 connects to r1c4 and r5c6.

2

Digits 3 and 3 are confined

Digit 3 in Row 1 is confined to r1c6 and r1c4. Digit 3 in Column 6 is confined to r1c6 and r5c6.

3

Either r1c6 is 3 or 3 fills both

Either r1c6 = 3, or both r1c4 and r5c6 contain 3.

4

Cells seeing the Firework lose 3

These candidates see the Firework pattern and cannot keep 3: r2c4.

5

Remove 3 from r2c4

Eliminate 3 from r2c4.

6

Result

Result after applying the technique.

Tips & Patterns

  • Firework patterns radiate from a single pivot point along a row and column - hence the name.
  • The pivot is at the center, with 'sparks' along both lines.
  • Look for digits with exactly 2 occurrences in both a row and column sharing a cell.