2026-07-28
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Puzzle guide
Full breakdown using the Pattern lab format — cell deductions, sign analysis, and strategy notes.
Overview
LinkedIn Tango #659 is the LinkedIn Tango daily for July 28, 2026. Tango is LinkedIn's balance puzzle: fill a 6×6 grid so every row and column has 3 suns and 3 moons, never three identical symbols in a line, and all = and × signs between neighbors are satisfied. This page includes the live board, a solved-board view, and a step-by-step Solution walkthrough. Difficulty: Easy. Estimated solve time: 3–5 min.
Answer
18 suns and 18 moons across the 6×6 grid.
This 6×6 board has 8 starting clues and 4 adjacency signs (1 equal, 3 opposite).
Analysis
Pattern lab — LinkedIn Tango #659. Grid 6×6. Constraint sample: 1 = edges, 3 × edges. Classification target: opposite-pair propagation. Deduction count: 28 forced cells beyond givens.
Sample technique distribution: row balance forces the last symbol (8); only one symbol still valid (7); the no-three-in-a-row rule blocks a repeat (5); a × sign demands opposites (3); column balance closes the line (3); an = sign links neighbors (1); two matching symbols sandwich this cell (1). Hypothesis (opposite-pair propagation): × pairs dominate this board — opposite signs force alternating symbols and quickly eliminate one option per linked cell.
Early samples: R1C4 → Moon (only one symbol still valid); R1C5 → Sun (a × sign demands opposites); R2C3 → Moon (only one symbol still valid). Mid-grid samples: R1C2 = Moon, R3C1 = Sun. Terminal samples: R6C5 → Moon and R6C6 → Sun. Each placement should cite a rule — naked single, balance, sign, or no-three.
Line balance check: Every row and column holds exactly 3 suns and 3 moons (row 1: 3 suns, 3 moons; row 2: 3 suns, 3 moons; row 3: 3 suns, 3 moons; row 4: 3 suns, 3 moons; row 5: 3 suns, 3 moons; row 6: 3 suns, 3 moons). That 3-and-3 split is the backstop when signs alone do not decide a cell.
Constraint verification: 1 equal signs require matching neighbors; 3 opposite signs require different symbols. A single broken edge means the grid fails even if row balance looks correct.
No-three rule pass: scan every row and column for three consecutive suns or moons — none appear in the completed grid. Sandwich cases (sun-moon-sun patterns around a filled pair) often force the middle cell and show up as two matching symbols sandwich this cell deductions on boards like this.
Lab result: Opposite-pair propagation. 18 suns and 18 moons across the 6×6 grid. Technique histogram: row balance forces the last symbol (8); only one symbol still valid (7); the no-three-in-a-row rule blocks a repeat (5); a × sign demands opposites (3); column balance closes the line (3); an = sign links neighbors (1); two matching symbols sandwich this cell (1).
Cells
Reasoning
Sun is ruled out: Two suns sit below — this cell cannot be sun.
Solving note
Sample 1: Moon at R1C4 because only one symbol still valid. Start from givens and adjacent signs.
Reasoning
The × sign between this cell and Row 1, column 4 means they must differ — Row 1, column 4 is Moon, so this cell is Sun.
Solving note
Sample 2: Sun at R1C5 because a × sign demands opposites. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit to the right — this cell cannot be sun.
Solving note
Sample 3: Moon at R2C3 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit to the left — a third sun here would break the no-three-in-a-row rule.
Solving note
Sample 4: Moon at R2C6 because the no-three-in-a-row rule blocks a repeat. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit below — this cell cannot be sun.
Solving note
Sample 5: Moon at R3C3 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit below — this cell cannot be moon.
Solving note
Sample 6: Sun at R1C3 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
The = sign between this cell and Row 2, column 6 means they must match — Row 2, column 6 is Moon, so this cell is Moon.
Solving note
Sample 7: Moon at R3C6 because an = sign links neighbors. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit below — this cell cannot be moon.
Solving note
Sample 8: Sun at R1C6 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
Row 1 still needs 2 more moons to reach the 3-and-3 balance, so the remaining open cells must be moons.
Solving note
Sample 9: Moon at R1C1 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Row 1 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons.
Solving note
Sample 10: Moon at R1C2 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Row 3 still needs 2 more suns to reach the 3-and-3 balance, so the remaining open cells must be suns.
Solving note
Sample 11: Sun at R3C1 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Row 3 still needs 1 more sun to reach the 3-and-3 balance, so the remaining open cells must be suns.
Solving note
Sample 12: Sun at R3C2 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit below — this cell cannot be sun.
Solving note
Sample 13: Moon at R2C2 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit to the right — this cell cannot be moon. Row 2 still needs 1 more sun to reach the 3-and-3 balance, so the remaining open cells must be suns.
Solving note
Sample 14: Sun at R2C1 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit to the right — this cell cannot be sun.
Solving note
Sample 15: Moon at R4C1 because only one symbol still valid. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit to the left — a third sun here would break the no-three-in-a-row rule.
Solving note
Sample 16: Moon at R4C4 because the no-three-in-a-row rule blocks a repeat. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule.
Solving note
Sample 17: Sun at R4C6 because the no-three-in-a-row rule blocks a repeat. Update row/column counts before the next placement.
Reasoning
Row 4 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons.
Solving note
Sample 18: Moon at R4C5 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
The × sign between this cell and Row 4, column 1 means they must differ — Row 4, column 1 is Moon, so this cell is Sun.
Solving note
Sample 19: Sun at R5C1 because a × sign demands opposites. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule.
Solving note
Sample 20: Sun at R5C5 because the no-three-in-a-row rule blocks a repeat. Update row/column counts before the next placement.
Reasoning
Two suns sandwich this cell — it must be Moon to avoid three suns in a row. Row 5 still needs 2 more moons to reach the 3-and-3 balance, so the remaining open cells must be moons.
Solving note
Sample 21: Moon at R5C4 because two matching symbols sandwich this cell. Update row/column counts before the next placement.
Reasoning
Row 5 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons.
Solving note
Sample 22: Moon at R5C6 because row balance forces the last symbol. Update row/column counts before the next placement.
Reasoning
Column 1 still needs 1 more moon for balance.
Solving note
Sample 23: Moon at R6C1 because column balance closes the line. Update row/column counts before the next placement.
Reasoning
Column 2 still needs 1 more sun for balance.
Solving note
Sample 24: Sun at R6C2 because column balance closes the line. Update row/column counts before the next placement.
Reasoning
Sun is ruled out: Two suns sit above — a third sun here would break the no-three-in-a-row rule. Column 3 still needs 1 more moon for balance. The × sign between this cell and Row 6, column 2 means they must differ — Row 6, column 2 is Sun, so this cell is Moon.
Solving note
Sample 25: Moon at R6C3 because a × sign demands opposites. Update row/column counts before the next placement.
Reasoning
Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule. Column 4 still needs 1 more sun for balance.
Solving note
Sample 26: Sun at R6C4 because the no-three-in-a-row rule blocks a repeat. Update row/column counts before the next placement.
Reasoning
Column 5 still needs 1 more moon for balance.
Solving note
Sample 27: Moon at R6C5 because column balance closes the line. Update row/column counts before the next placement.
Reasoning
Row 6 still needs 1 more sun to reach the 3-and-3 balance, so the remaining open cells must be suns. Column 6 still needs 1 more sun for balance.
Solving note
Sample 28: Sun at R6C6 because row balance forces the last symbol. Final open cell — grid complete after this.
Verification
Optimal deduction sequence length: 28. Constraint coverage: 4 edges, 1 equal / 3 opposite. Pattern: opposite-pair propagation.
Solve path
Phase 1: 6×6 Tango board with 8 locked clues and 4 adjacency signs — each row and column needs 3 suns and 3 moons with no three identical symbols in a line. Step 1: R1C4 → Moon (naked single). Sun is ruled out: Two suns sit below — this cell cannot be sun. Step 2: R1C5 → Sun (opposite sign). The × sign between this cell and Row 1, column 4 means they must differ — Row 1, column 4 is Moon, so this cell is Sun. Step 3: R2C3 → Moon (naked single). Sun is ruled out: Two suns sit to the right — this cell cannot be sun. Step 4: R2C6 → Moon (no-three rule). Sun is ruled out: Two suns sit to the left — a third sun here would break the no-three-in-a-row rule. Step 5: R3C3 → Moon (naked single). Sun is ruled out: Two suns sit below — this cell cannot be sun. Step 6: R1C3 → Sun (naked single). Moon is ruled out: Two moons sit below — this cell cannot be moon. Step 7: R3C6 → Moon (equal sign). The = sign between this cell and Row 2, column 6 means they must match — Row 2, column 6 is Moon, so this cell is Moon. Step 8: R1C6 → Sun (naked single). Moon is ruled out: Two moons sit below — this cell cannot be moon. Step 9: R1C1 → Moon (row balance). Row 1 still needs 2 more moons to reach the 3-and-3 balance, so the remaining open cells must be moons. Step 10: R1C2 → Moon (row balance). Row 1 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons. Step 11: R3C1 → Sun (row balance). Row 3 still needs 2 more suns to reach the 3-and-3 balance, so the remaining open cells must be suns. Step 12: R3C2 → Sun (row balance). Row 3 still needs 1 more sun to reach the 3-and-3 balance, so the remaining open cells must be suns. Step 13: R2C2 → Moon (naked single). Sun is ruled out: Two suns sit below — this cell cannot be sun. Step 14: R2C1 → Sun (row balance). Moon is ruled out: Two moons sit to the right — this cell cannot be moon. Step 15: R4C1 → Moon (naked single). Sun is ruled out: Two suns sit to the right — this cell cannot be sun. Step 16: R4C4 → Moon (no-three rule). Sun is ruled out: Two suns sit to the left — a third sun here would break the no-three-in-a-row rule. Step 17: R4C6 → Sun (no-three rule). Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule. Step 18: R4C5 → Moon (row balance). Row 4 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons. Step 19: R5C1 → Sun (opposite sign). The × sign between this cell and Row 4, column 1 means they must differ — Row 4, column 1 is Moon, so this cell is Sun. Step 20: R5C5 → Sun (no-three rule). Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule. Step 21: R5C4 → Moon (sandwich rule). Two suns sandwich this cell — it must be Moon to avoid three suns in a row. Step 22: R5C6 → Moon (row balance). Row 5 still needs 1 more moon to reach the 3-and-3 balance, so the remaining open cells must be moons. Step 23: R6C1 → Moon (column balance). Column 1 still needs 1 more moon for balance. Step 24: R6C2 → Sun (column balance). Column 2 still needs 1 more sun for balance. Step 25: R6C3 → Moon (opposite sign). Sun is ruled out: Two suns sit above — a third sun here would break the no-three-in-a-row rule. Step 26: R6C4 → Sun (no-three rule). Moon is ruled out: Two moons sit above — a third moon here would break the no-three-in-a-row rule. Step 27: R6C5 → Moon (column balance). Column 5 still needs 1 more moon for balance. Step 28: R6C6 → Sun (row balance). Row 6 still needs 1 more sun to reach the 3-and-3 balance, so the remaining open cells must be suns. Complete: 18 suns and 18 moons across the 6×6 grid. All = and × constraints satisfied — no row or column violates balance or the no-three rule.
Pattern
× pairs dominate this board — opposite signs force alternating symbols and quickly eliminate one option per linked cell.
Every row and column holds exactly 3 suns and 3 moons (row 1: 3 suns, 3 moons; row 2: 3 suns, 3 moons; row 3: 3 suns, 3 moons; row 4: 3 suns, 3 moons; row 5: 3 suns, 3 moons; row 6: 3 suns, 3 moons).
Learn more in Tango Puzzle Strategies →Takeaways
All 36 cells on 6×6 satisfy Tango rules. Deduction techniques: row balance forces the last symbol (8); only one symbol still valid (7); the no-three-in-a-row rule blocks a repeat (5); a × sign demands opposites (3); column balance closes the line (3); an = sign links neighbors (1); two matching symbols sandwich this cell (1).
4 signs on 36 cells — moderate sign density. Opposite-pair propagation boards favor × alternation.
× pairs dominate this board — opposite signs force alternating symbols and quickly eliminate one option per linked cell.
Solution
This 6×6 grid has 8 locked clues and 4 adjacency signs (1 equal, 3 opposite). 18 suns and 18 moons across the 6×6 grid. Every row and column holds exactly 3 suns and 3 moons (row 1: 3 suns, 3 moons; row 2: 3 suns, 3 moons; row 3: 3 suns, 3 moons; row 4: 3 suns, 3 moons; row 5: 3 suns, 3 moons; row 6: 3 suns, 3 moons). × pairs dominate this board — opposite signs force alternating symbols and quickly eliminate one option per linked cell. Use the Solution tab for a cell-by-cell reveal with live board updates and constraint reasoning, or the Solved board tab for the complete grid.