Graceful

One puzzle a day, and everyone gets the same one. Number the circles so that every line between them ends up with a different value. It takes thirty seconds to learn and a while to get good at.

The puzzle comes from graceful labeling, an idea from graph theory. Mathematicians have been trying to prove the graceful tree conjecture since the 1960s, and nobody has managed it yet.

1. Number every circle. Each circle gets its own number, from 0 up to the number of lines. No number is used twice.
2. Every line takes a difference. A line between 7 and 2 is worth 5.
3. Make every line different. You win when no two lines share a value. With ten lines, the values end up being exactly 1 through 10, each appearing once.

Lines that share a value glow in the same colour, so you can see what still clashes. Undo as much as you like.

• A new board every day. Difficulty climbs through the week, from a gentle Monday to Sunday's biggest board.
• Streaks. Solve each puzzle on its own day to keep your streak going.
• Catch up all week. The last seven days of puzzles are always free to play. A one-time purchase unlocks the full archive. It is not a subscription.
• Share without spoilers. Share your time and a grid of coloured blocks that shows the shape of your solve without giving away the answer.
• Built to be quiet. No accounts and no ads. Nothing is sent anywhere, and it works with no signal at all.

Questions, bugs, or a puzzle that looks wrong? Email gracefuldailypuzzle@gmail.com. Include your iOS version and the puzzle number from the top of the screen if it is about a specific board — that number identifies the exact puzzle.

Restoring a purchase

The archive unlock is a one-time purchase tied to your Apple Account, not to a device. On a new phone, or after reinstalling, open Archive → Unlock → Restore purchase. Nothing needs buying again. Make sure you are signed in with the same Apple Account used for the original purchase.

Progress and streaks

Progress is stored on the device only, so it does not follow you to a new phone and is lost if the app is deleted. The archive unlock is the exception: that is restorable, because Apple holds the receipt.

Last updated 26 August 2026

Graceful collects no data. There are no accounts, no analytics, no advertising, and no third-party SDKs of any kind. The app makes no network requests of its own — it works with no signal at all.

What is stored, and where

Which puzzles you have solved, your times, and your streak are written to a file inside the app’s own private storage on your device. That file is never transmitted anywhere. Deleting the app deletes it.

Purchases

The archive unlock is processed entirely by Apple. Graceful never sees your payment details, name, or email — it only asks Apple whether this Apple Account owns the unlock, and stores nothing about the purchase itself. Apple’s handling of that transaction is covered by Apple’s Privacy Policy.

Sharing a result

The share grid is text you choose to send, using the standard iOS share sheet. It contains a puzzle number, your time, and coloured blocks describing the shape of your solve. Nothing is sent unless you send it, and where it goes is up to you.

Children

Graceful is suitable for all ages. Since it collects nothing from anyone, it collects nothing from children.

Changes

If this policy ever changes, the updated version will be posted here with a new date. Any change that involved collecting data would arrive with a new version of the app, and would be described here first.

Contact

gracefuldailypuzzle@gmail.com