Tango strategy: how to solve Tango fast

The boards here use cats and dogs from Cats & Dogs, our free daily puzzle with the same rules as LinkedIn's Tango. Read cat for sun and dog for moon, and every move works the same way. Grey squares were filled already. A blue ring marks a square the move fills in.

The rules, in short:

• Every square holds a cat or a dog.
• No more than two alike side by side, across or down.
• Every row and every column has three cats and three dogs.
• An = between two squares means the same animal. A × means different ones.

New to the game? The LinkedIn Tango guide explains the rules with practice boards. The moves below come in the order our own solver tries them: quick ones first, slow ones last.

Moves you spot at a glance

These four solve most Easy boards on their own. Learn to see them without thinking.

1. Close off a pair

Two of the same animal side by side can't have a third next to them. So the squares at both ends of a pair must be the other animal. This is the most common move in the game, and it works down columns just as well as across rows.

A pair at the edge of the board has only one open end. That's still one free square.

2. Fill the sandwich

When two of the same animal sit one square apart, the square between them must be the other animal. If it matched, you'd have three in a row. Sandwiches are easy to miss because the two animals don't touch, so train your eye to look for "same, gap, same".

3. Follow a sign

An = means the two squares match. A × means they differ. When one side of a sign is filled, the other side is settled at once.

Notice what the = just did in row 2: it made two cats side by side. An = with one side known always makes a pair, so it always hands you the pair move straight after.

4. Follow a chain of signs

Signs pass information along. One filled square can settle a sign, the new square can make a pair, the pair fills a square next to another sign, and so on. Here a single dog fills a whole row:

1. The = copies the dog into column 3.
2. That makes a pair of dogs, so columns 1 and 4 are cats.
3. The × after the cat in column 4 makes column 5 a dog.
4. The row now has three dogs, so the last square is a cat.

The lesson: when you fill a square, don't look away. Check its signs, then check whether it made a pair or a sandwich. Most of a board falls like this, one square setting off the next.

Moves that need counting

Nothing on the board points at these. You have to count.

5. Count to three

Each row and column holds exactly three cats and three dogs. Once a line has three of one animal, every gap left in it is the other animal.

Counting is the move people forget most, because no pair or sign draws your eye to it. Make it a habit: each time a line gets its third cat or third dog, fill the rest of it before you move on.

6. The last two squares

When a line is down to two gaps and already has two of each animal, the gaps need one cat and one dog. Think of them as joined by an invisible ×: settle either one, and the other is the opposite.

So don't stare at the line itself. Look along the crossing line of each gap and pick whichever is easier to settle. Here, row 6 needs one of each. The right-hand gap sits under two dogs in column 6, so it must be a cat. Row 6 then has its three cats, and the other gap is a dog.

Moves for Medium and Hard boards

When the quick moves run dry, these find the next square.

7. Try every way to finish a line

Pick a line with a few gaps. Work out the ways to finish it that break no rule. If every one of them puts the same animal in a square, that square is settled. Our hints describe it as "Try every way to finish the row without breaking a rule."

Take a row that starts and ends with a cat. It needs one more cat and three more dogs in the four squares between. Three dogs can't sit together, so the cat has to split them: dog, cat, dog, dog, or dog, dog, cat, dog. You don't know yet which one is right. But both put a dog next to each end cat, so those two squares are settled.

Lines with three or four gaps are the best place to try this. With more gaps there are too many ways to list. Signs inside the line help too: a × between two gaps means one of each, which often tells you what the other gaps need.

8. Work rows and columns together

Every square sits in one row and one column. A move in a row often sets up a move in a column, and back again. After each move, check the crossing line of every square you filled.

Here row 3 already has its three dogs, so both gaps become cats. The one in column 6 lands under another cat, which makes a pair, and the pair settles the squares above and below it. Two moves, two different lines.

9. Test a square

Hard boards hide a step none of the other moves can reach. Pick a square, imagine a cat in it, and follow the quick moves. If a rule breaks, the square must be a dog. Our hints put it this way: "A cat here would break a rule a few moves later."

This is not guessing. You test one idea in your head and only write down what the test proves. Try it on the corner below:

1. Imagine a cat in the top-left corner. Row 1 now starts with two cats, so its third square is a dog.
2. Column 1 also starts with two cats, so its third square is a dog.
3. The × under the new dog in row 1 makes the square below it a cat.
4. The = beside the new dog in column 1 makes the square beside it a dog.
5. Now look at row 2, column 2. Its × to the right says it's a dog. Its × below says it's a cat. It can't be both.

The cat failed, so the corner is a dog. Pick test squares where the chain will be short: next to signs, or in a line with only a few gaps. If the test runs out of moves without breaking a rule, it proves nothing, so rub it out and try another square.

Habits for solving Tango fast

Knowing the moves is half of it. The other half is looking in the right place first.

• Scan in a fixed order. Pairs and sandwiches first, then signs, then counts. Only then look at whole lines.
• Follow every new square. Check its signs, its row and its column before you look anywhere else.
• Finish nearly full lines. A line with one or two gaps is quick to settle and often unlocks its crossing lines.
• Count as you go. Keep a rough tally of each line's cats and dogs, so you notice the third one when it lands.
• Never guess. A wrong guess has to be found and undone, which costs far more than a moment's thought.
• Don't use the matching-rows rule. Some Takuzu puzzles ban two identical rows. Tango doesn't state that rule, and Cats & Dogs doesn't use it.
• Use hints to learn. Our Hint button shows the next square and says why it works. If it keeps showing the same kind of move, that's the one to practise.

For the habits that slow most people down, read seven common Tango mistakes.

Where to practise

LinkedIn gives you one Tango a day. To get faster you need more boards than that. Every one of these is free, with no app and no account:

• Today's Cats & Dogs: three new boards a day. Use Easy for moves 1 to 5, Medium for whole-line logic and Hard for testing a square.
• Endless: a fresh board each time you finish one, at the level you pick.
• Daily solutions: every past board solved step by step, with a reason for each move.
• The Tango solver: copy in a board you're stuck on, and it explains the next step.
• The archive: every board we've published, all still playable.

The same puzzle also goes by Takuzu and Binairo. If you know those names, see Takuzu and Binairo online. For other puzzles in the same family, see our list of games like Tango.