How to play

Six numbers, six cells, no guessing.

Lemma is a 6x6 Sudoku. Every cell gets a number from 1 to 6, and the same number never repeats where it can see itself. That is the whole game.

The rules

The board has six rows, six columns and six boxes. Each box is 2 rows tall and 3 columns wide. Every row, every column and every box holds the numbers 1 to 6 exactly once.

Each row holds 1 to 6 once.

Each column holds 1 to 6 once.

Each box holds 1 to 6 once.

Some numbers are given. Fill the rest by logic. Every lemma has exactly one answer and can be proven without guessing. A number turns red only while it clashes with another in its row, column or box.

The words we use

lemma: A puzzle: one 6x6 Sudoku.
daily lemma: The lemma everyone plays on their own date. Free forever.
proven: Solved: every cell is right.
unassisted: Proven with no hints.
elegant: Proven with no hints and no corrections.
hint: A nudge that shows its reasoning: the rule and the cell, never the answer.
correction: A number you placed that is not the answer.
sequence: Consecutive daily lemmas you have proven.
freeze: Saves your sequence on a day you miss.
theorem: Every 36 proven daily lemmas make one, named after you. It uncovers a hidden figure and gives a reward.
notebook: The screen that holds your progress.
co-authors, circles: Your people, and the private groups where you share times, never numbers.
corollary: Lemma Plus: extra lemmas at easy, medium, hard and expert, made on your phone.
archive: Lemma Plus: every past daily lemma.
Lemma Plus: The optional subscription. Everything else is free.

The two techniques the hints use

A hint never gives the answer away. It names a technique, so next time you spot the move yourself. Both examples below come from lemma #214's starting position.

Naked single

A cell where only one number is still possible.

Look at row 4, column 3. Its row already holds 1 and 6. Its column holds 2, 3, 5 and 6. Its box holds 2 and 6. Between them they cover 1, 2, 3, 5 and 6, which leaves one number: the 4.

Hidden single

A number that has only one cell left in a row, column or box, even if that cell could hold other numbers too.

Look at the bottom left box and the number 4. Every other empty cell in it can already see a 4 in its row or column, the ringed numbers on the board. The 4 has one place left: row 6, column 2, even though that cell could hold other numbers too.

How the day works

A new lemma arrives at midnight, your local time. A player in Tokyo and a player in Lisbon each get lemma number n on their own date, and it is the same puzzle.
Prove a lemma every day and your sequence grows. If you miss a day, a freeze saves the sequence.
Every 36 proven daily lemmas make a theorem in your name. Each one uncovers a hidden figure and gives a reward.
Share the proof, not the numbers: the share card shows your time and the order of your proof, never a digit.

Want to try it now? Prove a small lemma on the home page, or get the app.