# Kissing Circles — Descartes Puzzle | Mathallery

Source: https://mathallery.com/games/apollonian/

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# Kissing Circles

Descartes · 30 levels

Fill the gaps of a fractal with whole-number circles.

## How to play

- Every circle shows its bend: bigger bend, smaller circle. The big outer circle bends the other way, so its bend is negative.
- A gap between three touching circles takes the circle with bend 2 × (sum of the three) − the circle on the other side.
- Tap the right bend in the tray to grow the glowing gap's circle. A wrong bend costs a spark ✦; lose all three and the gasket resets.

The circle on the other side touches the same three circles. Watch the minus signs: taking away −1 adds 1. A hidden “?” circle sits in a gap too, so work it out first.

[Open Kissing Circles](https://mathallery.com/#/play/apollonian/1)

Teeter, Tint and Echo Heist are free starters. Other games unlock through earned game choices or permanent packs. Your progress stays in the browser; optional sign-in saves it to your website account.