---
title: 'The Lattice Bacteria Puzzle'
source: 'https://youtube.com/watch?v=d0ai33oqqDE'
video_id: 'd0ai33oqqDE'
date: 2026-08-10
duration_sec: 62
---

# The Lattice Bacteria Puzzle

> Source: [The Lattice Bacteria Puzzle](https://youtube.com/watch?v=d0ai33oqqDE)

## Summary

The video presents a mathematical puzzle involving bacteria on a grid. The goal is to clear a 3x3 box starting from a single cell, using a specific replication rule. The puzzle is part of a collaboration with MoMath and will be solved in a follow-up video.

### Key Points

- **Replication Rule** [00:01] — A bacterium can replicate into the two spots above and to its right, but only if both are empty.
- **Puzzle Goal** [00:27] — The goal is to clear a 3x3 box with corners at (0,0), (0,3), (3,3), and (3,0), starting from a single cell at the origin.
- **Collaboration and Follow-up** [00:41] — The puzzle is part of a monthly series with MoMath, and Peter Winkler will host a follow-up discussion.

## Transcript

bacteria sitting on a grid. At any [music] point, you can select one of them, and if the spaces one above and one to the right are both empty, you can make it replicate, [music] populating both of those spots with its children
from. The rule is that only one cell is those two target spots is currently blocked for a given bacterium, it can't replicate. But as soon as both of them clear out, it's free to do so.
>> Here's my puzzle for you. Suppose you begin with just one cell at the origin, and your goal is to eventually clear out this box here, the one with corners at 0 this box here, the one with corners at 0 0, 0 3, 3 3, and 3 0. What is the
smallest number of moves required [music] to do so? To be clear, all 16 of these lattice points have to end up empty. This is part of a monthly series collaboration with MoMath. The mathematician Peter Winkler will host a
[music] and I'll post my own video of the solution here sometime next month.