The lattice bacteria puzzle

2026-02-18 · Source: 3Blue1Brown · Field: Science & Research — Mathematics & Computational Sciences · Depth: Fundamental Awareness, quick

Summary

A puzzle game involves bacteria on a grid where a selected bacterium can replicate into the spaces one above and one to the right, provided both target spots are empty. The original spot is then vacated, and each grid point can only hold one cell. The puzzle starts with a single cell at the origin (0,0) and challenges players to clear out a 4x4 box defined by corners at (0,0), (0,3), (3,3), and (3,0). The objective is to determine the minimum number of moves required to empty all 16 lattice points within this specified box. This puzzle is part of a monthly series, with a solution explanation to be hosted by mathematician Peter Winkler.

Key takeaway

For puzzle enthusiasts or computational problem solvers, understanding the precise replication rules and grid constraints is crucial. Your strategy should focus on minimizing redundant moves and anticipating future blockages to efficiently clear the 4x4 box. Consider exploring different move sequences to find the optimal path to an empty grid.

Key insights

A grid-based puzzle challenges players to clear a 4x4 box using specific bacterial replication rules.

Principles

• One cell per grid point
• Replication requires two empty target spots

In practice

• Simulate grid movements
• Track empty/occupied spots

Topics

• Lattice Puzzles
• Cellular Automata
• Optimization Problems
• Grid-based Games

Best for: Research Scientist, Software Engineer, General Interest

Related on AIssential

• Bacteria Grid Puzzle Solution — A weighted sum invariant proves the impossibility of clearing certain grid configurations in a bacteria replication puzzle.
• Discovering Lattice Reduction Strategies via Self-Play — Deep reinforcement learning can discover superior, generalizable lattice reduction strategies beyond traditional algorithms like LLL.
• Ponder This Challenge - June 2026 - The Superhero Team Movies — Designing superhero movie franchises to minimize action sequences covering all hero combinations.
• Transforming Constraint Programs to Input for Local Search — Automatically generating local search neighborhoods from constraint specifications by linking symmetry properties reduces human intervention in combinatorial optimization.
• Solution to the ladybug clock puzzle — All numbers on a clock face (excluding the start) are equally likely to be the last touched in a random walk.
• Deterministic Event-Graph Substrates as World Models for Counterfactual Reasoning — Deterministic replay over typed event deltas enables auditable, exact counterfactual world modeling without learned latent simulation.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by 3Blue1Brown.