Tango Solver

Try the tango solver

What Tango's rules actually constrain

Tango looks like a two-colour Sudoku but the logic is closer to a binary puzzle, and the solver treats it as one. Every row and every column must contain exactly three suns and three moons. No row or column may contain three of the same symbol in a row — two together is fine, three is not. An = sign between two cells forces them to match; an × forces them to differ. That is the whole rule set, and the third rule does far more work than newcomers expect: on a six-cell line, "no three alike" plus "three of each" leaves only fourteen possible patterns out of sixty-four.

Internally the solver is a straightforward backtracking search. It visits the empty cells in reading order, tries a sun and then a moon in each, and keeps a value only if every row and column still has at most three of each symbol, no three alike in a line, and every sign whose two cells are both filled is respected. When a cell has no legal value it steps back and tries the other symbol in the previous cell. It stops at the first complete grid, so it shows one answer and does not check for a second — which is why a sign entered on the wrong border can still produce a grid the game rejects. The moves a human uses, and the order they work in, are on the Tango guide; the solver doesn't show steps.

The tool is built for 6×6 only, which is the size of every one of the 37 Tango boards in our archive (3 September – 10 October 2026). Larger binary puzzles exist elsewhere under names like Takuzu and Binairo, where grids commonly range from 4×4 to 20×20 (Wikipedia) and standard rules also ban identical rows and columns — a rule LinkedIn's Tango does not have.

Entering the board without introducing a mistake

A Tango board carries two kinds of information and both must be copied exactly. The givens are the pre-filled suns and moons; in our archive a board had between 4 and 12, most often 8. The signs sit on the border between two cells — on every archived board, two cells sharing an edge, never diagonal — and there were 2 to 8 per board, most often 4. The signs are the part people mis-enter, because on the real board they are small and it is easy to attach one to the wrong pair of cells. In the tool, a sign is placed by tapping the circle drawn between the two cells, so look at which two cells the circle touches before you tap.

Two checks catch nearly every input error. First, count the givens on the real board and compare with your entry, where given cells are shaded. Second, after solving, read the solved grid against the signs on the real board: every = should join two identical symbols and every × two different ones. If one does not, the sign was placed on the wrong border, and re-placing it will usually change the answer.

When the solver says the board is inconsistent

The message means the givens and signs you entered cannot all be true at once. The real board has a valid fill, so one of the inputs is wrong. Check in this order:

• A given placed in the wrong cell — most often one row or column off, because the board was entered from memory rather than side by side with the game.
• A sign attached to the wrong pair of cells, usually the pair one step along the same line.
• A sun entered as a moon or vice versa; the icons are small on a phone and the mistake is common late at night.
• A sign that does not exist on the real board, left over from a previous solve. Use the Clear button between puzzles; it removes the givens and the signs.

What to take from the solution

The solved grid is more instructive than it looks if you ask one question of it: which cell should have been the first move? On 35 of the 37 archived boards there was a cell forced immediately by two matching givens — either side by side or with one blank between them in a line. If you started somewhere else and worked around to it, you have found the habit to change.

The second thing to look for is the counting move. Late in a board, a row that already holds three suns has its remaining cells fixed as moons whether or not the adjacency rule says anything, and it is easy to keep hunting for adjacency moves when a count would finish the line. Both deductions, plus the sign-chain move that links a run of = and × signs into one decision, are set out with examples on the Tango guide, and the Tango archive has past boards to try them on.

A real board: Tango #696

Tango #696, on 3 September 2026, had eight givens and two signs, and its top row finished sun, sun, moon, moon, sun, moon. The first forced cells came from pairs of matching givens. Row 1 had moons side by side in columns 3 and 4, so columns 2 and 5 of that row are suns. Column 2 had moons in rows 2 and 3, so row 4 of that column is a sun. Column 5 had suns in rows 4 and 5, so rows 3 and 6 of that column are moons. That gives column 5 three suns (rows 1, 4 and 5), which makes row 2 of it a moon; and row 6, now holding moons in columns 4 and 5, takes a sun in column 6.

Seven cells from pair and count moves, and then the basic moves run out: the board's two signs — an = in column 3 and an × in column 4, both between rows 3 and 4 — sit among blanks. From there the line check does the work, listing the legal patterns for each row and column until cells agree. When you enter #696 from the archive and press solve, the answer appears; the useful exercise is to cover the solution and see how far the pair and count moves carry you before you need the line check.

Difficulty across the week

LinkedIn does not label Tango puzzles by difficulty. In our archive the sign, pair, gap and count moves alone finished 6 of the 15 Monday–Wednesday boards and none of the 22 Thursday–Sunday boards. Givens ranged from 4 to 12 per board and signs from 2 to 8, and three of the four boards with only four givens fell on a Sunday. The line check — listing the legal patterns for a row or column — finished 30 of the 37 boards with no trial at all; the solver needs neither, since it searches.

If you do reach a point where neither the basic moves nor the line check places anything, a what-if is legitimate: put one value in the most constrained cell and follow every consequence. If a rule breaks, the other value is correct; if the board completes without breaking a rule, you have an answer. Either way, propagate fully before you decide.

Wrong moves the solver quietly exposes

Comparing your grid to the solved one after a slow board tends to reveal one of a small number of errors:

• Placing a symbol to "balance" a row that already has two of it, when the adjacency rule had not yet forced anything. Counting only bites once a line holds three; two of a kind tells you nothing on its own.
• Treating a sign as one-directional. An = between cells A and B constrains both; people fill A from the sign and then forget to check that B's line still allows the same symbol.
• Missing the two-apart pattern (sun, blank, sun) because the eye looks for adjacent pairs. The gap version forces the middle just as strongly.
• Reading a sign as belonging to the wrong pair when two signs sit near each other. On a phone the circles are small; zoom in before entering them.
• Assuming symmetry. Nothing in LinkedIn's rules says a solution is symmetric; the solver has no notion of symmetry and neither should you.

Solving without the solver: the three deductions in order

The three moves below are the ones a human uses. On the six archived boards they finish outright, nothing else is needed; on the rest they do the early work before the line check takes over. First, the sandwich: any line with two matching symbols adjacent, or two matching symbols with one blank between them, forces the cell on either side or in the middle to be the other symbol. Scan every row and column for it before doing anything else, because it needs no counting and no signs. Second, the sign chain: follow every = and × from any cell that is already filled; an = copies the symbol, an × flips it, and a run of signs can carry one symbol across half the board. Third, the count: any line holding three of a symbol has its blanks filled with the other.

Beginners often apply these in the wrong order — count first, because it feels like the rule — and stall, because counting rarely fires from the givens alone: on 27 of the 37 archived boards no line started with three of a symbol. The sandwich fired immediately on 35 of the 37, and each cell it fills feeds the sign chain, which feeds the count. When all three are exhausted and blanks remain, list the legal patterns for the line with the fewest blanks. The Tango guide has the moves drawn on real boards, and the answers page shows the current puzzle solved.

One last habit worth stealing from the rules themselves: never mark a cell tentatively. If every symbol you write is a consequence of a rule — no pencil marks, no "probably a sun" — you stop undoing work. The Tango archive has past grids to practise that on.