Collinear

Points on the same line can't share a number.

How to play

Each board is a set of points and the lines through them. Your job is to give every point a number so that no two points on the same drawn line share a number. Only drawn lines count.

1. Call it

Before you touch the board, guess the fewest numbers that can do the job. The longest line is an obvious lower bound, but some boards need more than that. The clock starts as soon as the board appears, so studying it counts toward your time. It pauses whenever the board isn't on your screen.

2. Prove it

Fill the board using only the numbers 1 to your guess. Pick a number from the palette, then tap points. Tap a point again to clear it. On a keyboard, the digit keys choose a number.

If you're stuck because your guess is too low, raise it. The board keeps track of how far off your first call was. A call only counts as proven if you finish without using any number above it.

3. Share

Today's board is the same for everyone. Your share card shows how close your call was and your time, without giving away the answer: 🟩 means you called it exactly, each 🟨 is one number too many, each 🟥 is one too few. 🟧 means your call was possible, but you raised and finished using more numbers than you called.

Play again

After finishing, Play again starts a fresh round from the guess step, so you can look for a different labeling or hand the board to a friend. Each round gets its own result and share card. On the daily board, the saved result and streak on your device come from the first attempt. On levels, a round that earns more stars replaces your saved result. The game also tells you whether each new labeling is genuinely different or just an earlier one with the numbers renamed.

Streaks and stats

Finish the daily board on consecutive days to build a streak. Streaks of 3, 5, 7, 10, 14, 30, 50 and 100 days earn polygon badges with that many sides. The Stats tab shows your history, how your calls have gone, your solve times and the achievements you've unlocked. Stats are saved in your browser on this device.

Difficulty

Monday and Tuesday boards are gentle. Wednesday to Friday mix in traps. Weekend boards always need more numbers than their longest line.

Feedback

Use the Report a bug and Suggest an idea links at the bottom of every page. They open a short form with your board number and device already filled in, so all you need to write is what happened.

Where the math comes from

Coloring points so every line is rainbow is the setting of the Erdős–Faber–Lovász conjecture, proved for large boards in 2021 by Kang, Kelly, Kühn, Methuku and Osthus. The Levels tab includes two classical configurations, Pappus and Desargues.