Firework

Firework

Master

Associated Techniques

What Is the Firework Technique?

The Firework exploits a pattern where a digit has exactly two candidate positions in both the row and the column of a single pivot cell. The pivot sits at the intersection, with one wing along the row and one along the column. The digit must appear in at least one of these three cells.

The Firework Pattern in Detail

Pivot P at the intersection. Row wing W1 (the other candidate in the row). Column wing W2 (the other candidate in the column). Both links are strong links. Two strong links share a common endpoint at the pivot.

How the Firework Logic Works

Case 1: Pivot has the digit. Then the digit is placed at P, so any cell seeing P cannot contain that digit.

Case 2: Pivot does not have the digit. Because the pivot is one end of a strong link in both its row and its column, the row wing W1 and the column wing W2 must both have the digit.

Either way, at least one of {P, W1, W2} contains the digit. A target can be eliminated if it sees P and also sees at least one wing. If P is true, the target is removed by P; if P is false, the visible wing is true and removes the target.

How to Find Firework Patterns

For each digit, find cells where both the row count and column count equal exactly 2, counting the cell itself. That cell is the pivot. The other candidate in the pivot's row is the row wing, and the other candidate in the pivot's column is the column wing.

After finding the three-cell firework, search for targets that see the pivot and at least one wing. The target does not need to see both wings, which is what makes Firework different from many wing techniques.

Look for a cross-hair or plus-sign shape in the pencilmarks.

Why the Firework Technique Is Rare

Requires exactly two candidates in both a row and column with one cell in common, plus an elimination target. Each condition narrows possibilities considerably.

Difficulty Rating and Context

Level 8 (Expert). Harder than basic wings and unique rectangles because the intersection pattern is less obvious. Simpler than chains because it involves only three cells. Related to Two-String Kite and Empty Rectangle conceptually.

Summary

The Firework is a row-column intersection pattern. A pivot forms strong links with two wings. Any candidate seeing the pivot and at least one wing is eliminated. Level 8 (Expert), rare but clean.

Associated Techniques