Each row and column needs equal numbers of the two symbols. Three identical symbols cannot appear consecutively in a row or column. An equals connector requires matching symbols; an X connector requires different ones. In the examples S means sun, M means moon, and ? is unfilled. These are constructed local exercises, not today's board.
Start with the no-three rule
S S ? → S S M ? M M → S M M S ? S → S M S
The first two cases stop a pair becoming a run of three. The third case is a sandwich: placing S in the middle would create S S S, so the middle must be M. These are local deductions; they do not require you to know the rest of the row.
Do not turn this into an alternating-symbol rule. S S is legal. So is M M. Only a run of three or more is excluded by this constraint, and diagonal lines do not count as rows or columns.
Use quotas without guessing the order
In a six-cell row, each symbol must appear three times. Once three suns are placed, every remaining cell must be a moon. But if two blanks must contain one of each symbol, their order is still unresolved until another constraint distinguishes them.
S M S ? ? S Three suns already placed. The blanks must both be M. Result: S M S M M S
A complete-looking row can conflict with a column. After filling a quota, examine the crossing columns immediately, then propagate any resulting forced placements. Do not wait until the entire board is filled.
Combine connectors with row counts
An equals connector between two blanks does not tell you which symbol they contain. It reduces the possibilities to S S or M M. An X reduces them to S M or M S. A known symbol at either end resolves its partner immediately.
Consider a six-cell row with the filled symbols S, S, M, M and exactly two remaining cells connected by X. The quota requires one sun and one moon, so X adds no new ordering information. If those same two blanks were linked by equals instead, the current filled choices would be inconsistent: neither equal pair could restore balance. That is a reason to revisit an earlier placement, not to ignore the connector.
Follow a connector chain carefully
S = ? X ? S = S X M
A chain with an even number of X links returns to the starting symbol; an odd number switches it. Equals links do not change that parity. This can relate two distant cells before either is resolved. However, a chain of all unknown symbols remains ambiguous until a count, a no-three pattern, or a known cell anchors it.
A practical solving loop
- Scan rows and columns for pairs and sandwiches.
- Propagate known symbols through connectors.
- Count each nearly completed row and column.
- Check new placements against all three constraint types.
- If nothing changes, inspect what a short connector chain implies about a row's remaining quota.
Do not add rules from another binary puzzle. In particular, do not assume rows must all be different unless the current game instructions explicitly require it. The evidence for a placement must come from this game's constraints.
Repair an error and learn from it
When a row ends with four suns, start with the last uncertain placement contributing to that count. If a connector is broken, trace the chain back to its first assumed symbol. If a triple appears, check whether a quota deduction overlooked a column. Keep a short note of the failed rule rather than merely correcting the final symbol.
Rule reference: LinkedIn Help: playing Tango. Our sketches explain individual deductions and are not complete official puzzles.
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