TWO RULES, TWO SYMBOLS
A Takuzu is a square grid — ours is 6×6 — and every cell ends up holding either a 0 or a 1. That's the whole alphabet. Two rules keep them in line:
- No three in a row. You can never have three of the same symbol touching in a line — no 0 0 0 and no 1 1 1, going across or down. Pairs are fine; three is the wall.
- Equal numbers of each. Every row and every column ends up with the same count of 0s and 1s — on a 6-wide grid that's three of each. (There's a third tidy-up rule — no two rows or columns identical — but you almost never need it to get going.)
That's it. And here's the lovely part: because there are only two options, ruling one out is the answer. Every square you can't make a 0, you've just made a 1.
LET'S ACTUALLY SOLVE ONE — STEP BY STEP
Here's a real Takuzu. Some squares are filled in to start you off; the rest are blank. We never stare at the whole grid — we just hunt for a pair sitting next to a gap.
The starting grid — violet squares are 0s, teal squares are 1s, the rest are yours to fill.
Step 1 — a pair points at the next square.
Look at the second row: there are already two 0s sitting side by side. The square right after them can't be another 0 — that would make 0 0 0, three in a row, which is illegal. So it has to be a 1. A touching pair always tells the square next to it what it isn't — and with only two choices, that's the answer.
Step 2 — a square caught between two of the same.
Same rule, sneakier angle. In the third column a blank square is sandwiched between a 1 above and a 1 below. Make it a 1 and you've got 1 1 1 down the column — no good. So it's a 0. Worth remembering: a gap squeezed between a matching pair is always the other symbol.
Step 3 — counting finishes a line.
Back to that second row. With the squares we've filled it now holds three 0s — and a 6-wide row is only allowed three. It's full up on zeros, so whatever's left can only be a 1. This is the balance rule doing the work: the moment a line has all three of one symbol, every remaining square is the other.
And that's the entire game — those two ideas, over and over. Spot a touching pair and fill the gap beside (or between) it; count a line that already has its three and fill the rest. Each square you drop in makes a new pair or finishes a count somewhere else, so it snowballs:
Halfway and rolling — every new square sets up the next.
Done. Three 0s and three 1s in every row and column, and not a single triple in sight. 👻
WHEN NOTHING'S OBVIOUS — TWO MORE NUDGES
Early on the pairs and counts do plenty. When they dry up, these two keep you moving — still no guessing.
1. Avoid the triple before it happens.
You don't need a finished pair to use rule one. If a square is a 0, and putting a 0 two squares along would trap the gap between them into making a triple, that gap is already decided. Reading one move ahead — "if this were a 0, that one would have to be 0 too, and then I'm stuck" — cracks a lot of lines.
2. Count what's left, not just what's there.
The balance rule cuts both ways. A 6-wide row needs three 0s and three 1s, so if it already has two 1s and only two empty squares left after a filled stretch, you often find one of those gaps is forced just to reach three of a symbol without breaking the no-triple rule. Whenever a line is nearly full, stop and count both symbols — the answer is usually hiding in the tally.
So the whole loop is: hunt for touching pairs and fill the gaps they forbid, finish any line that already has its three of a symbol, and when it stalls, count one move ahead. Never a guess — with two symbols, every square has a reason.
THAT'S IT — GO DO ONE
Two symbols, two rules: no three in a line, equal counts each way. Find a pair, fill the gap; finish a count, fill the rest. The first time a single pair topples a whole row it's oddly satisfying. No words, no maths homework, no ads mid-puzzle — just you, two little digits, and a ghost who's quietly chuffed when the grid balances out.