# Hailstone — Halving Puzzle | Mathallery

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

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# Hailstone

Halving · 30 levels

Grow coral from 1 with ×2 and (n−1)÷3.

## How to play

- Every number falls back to 1: halve it if even, else 3n + 1. Each number's path is a branch of coral.
- Grow coral up from 1 by undoing those steps: ×2 bends left, (n − 1) ÷ 3 bends right (only when the answer is whole and odd).
- Match the ghost branch, then reach every pearl using exactly the polyps you have. ↓ walks back down.

To reach a pearl, work forward from it: 52 → 26 → 13 → 40 → … → 1. Then build that list backwards. Two pearls often share a trunk, so follow one until the paths split.

[Open Hailstone](https://mathallery.com/#/play/hailstone/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.