About Lacuno

Lacuno looks like a grid game. Underneath, it's a small piece of algebra dressed up to look like one.

It's not arithmetic

The three symbols — ▲, ■, ● — don't stand for numbers. They're three abstract states, and the combination table defines how any two of them combine.

Mathematicians call this the cyclic group of order three. You don't need to know that. You need to know that ■ leaves anything unchanged, two ▲s make a ●, two ●s make a ▲, and three of anything makes ■.

The depth underneath

What looks like a small three-symbol grid is actually an exercise in one of the foundational structures of algebra. If you studied maths at school, the mental shape of a Lacuno solve will feel familiar. If you didn't, you're doing it anyway.

The more you play, the faster you get — not because you've memorised the table, but because you've started to see patterns in how the symbols behave. Those patterns are the structure of the group. You're learning real algebra by feel.

How is it different from Sudoku?

Sudoku is about variety: each digit must appear exactly once. You reason about what's missing.

Lacuno is about result: each line must combine to a specific target. You reason about what balances. A row of five ■s is perfectly fine, if the target is ■.

What you're actually doing

Every move you make in Lacuno is a move algebra asks of you. You substitute a value into an unknown. You check it against two constraints at once. You work backwards from a target. When you put the right symbol in the right cell and the row resolves, you've done the same thing as solving for x in an equation — just without the notation.

That's not a marketing claim. It's the mechanic. The symbols are abstract; the thinking is the real thing. Whether it transfers to school algebra is a separate question, and an honest one — no one's tested it on Lacuno specifically. But the structure is there, every time you play.

Does it make you smarter?

Probably not in the way brain-training apps claim. The research on puzzles improving general intelligence is weaker than the marketing suggests — you mostly get better at the thing you practise, not everything else. Some of the best-known brain-training apps have been fined for overstating what they do.

What I can honestly say is that Lacuno uses the same moves as algebra — substitution, consistency-checking, inference from what you already know. Whether that transfers to anything else is a real open question.

What I know for sure is that when it clicks, it feels good. That's reason enough to play.

Questions people ask

Is Lacuno free to play?

Yes. The web version is free and always will be. No ads, no subscriptions, no account needed.

Do I need an account?

No. Open the page and play. Your progress is saved in your browser, on your device.

How long does a puzzle take?

It depends on you. The daily is designed to be a short break, not a long session.

Is there a new puzzle every day?

Yes. A new puzzle appears at midnight UTC. Every player in the world sees the same one.

Is Lacuno like Sudoku?

They're cousins, not twins. Sudoku asks you to avoid repetition — every digit once per line. Lacuno asks you to hit a target — the symbols in each line must combine to a specific result. Different rule, different reasoning.

Can I play Lacuno on my phone?

Yes. The web version works on any phone browser. A native iPhone app with unlimited play is coming — sign up on the app page.