What is the goal of the bacteria puzzle presented?

The goal is to clear out a specific box on the grid, with corners at (0,0) and (3,3), and also the point (3,0). All 16 lattice points within this defined area must end up empty.

What is the smallest number of moves to clear the lattice box?

The puzzle asks for the minimum number of moves required to vacate all 16 specified lattice points. The exact solution will be explained in upcoming videos.

Who is collaborating on this monthly puzzle series?

This puzzle is part of a monthly series created in collaboration with Moath. The mathematician Peter Winkler will also host a session to explain the solution.

The lattice bacteria puzzle

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Education2 min read2 min video

Feb 18, 2026|759,577 views|23,490|815

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Key Moments

TL;DR

Bacteria replication puzzle on a grid: Clear a 3x3 box with minimal moves.

Key Insights

Bacteria can replicate to adjacent empty cells (up and right).

Replication requires both target cells to be empty.

The goal is to clear a 3x3 grid of all bacteria.

The puzzle asks for the minimum number of replication moves.

This is a monthly puzzle series in collaboration with MoMath.

THE GAME MECHANICS

The core of the puzzle involves a grid where bacteria reside. A bacterium at a specific point can replicate if the space directly above it and the space directly to its right are both unoccupied. Upon replication, the original bacterium vacates its spot, and its 'children' populate these two newly empty spaces. This mechanic implies movement and expansion within the grid, governed by the availability of adjacent cells.

RULE OF SINGLE OCCUPANCY

A critical constraint in this game is that only one bacterium can occupy any given point on the grid. If either the cell above or the cell to the right of a bacterium intended for replication is already occupied, that bacterium cannot replicate. This rule ensures space management and introduces a strategic element, as blocking adjacent cells can prevent further proliferation.

THE PUZZLE OBJECTIVE

The specific challenge presented is to start with a single bacterium positioned at the origin (0,0). The ultimate aim is to have all sixteen lattice points within a 3x3 box — defined by corners (0,0), (3,3), and (3,0) — become empty. This means every bacterium must eventually move out of this designated area or cease to exist within it.

THE MINIMUM MOVES REQUIREMENT

The puzzle doesn't just ask if the 3x3 box can be cleared; it demands the most efficient solution. Participants must determine the smallest possible number of replication moves required to achieve the objective of an entirely empty 3x3 grid. This optimization aspect suggests that a brute-force or inefficient approach might lead to a solution, but not the one sought.

COLLABORATION AND FUTURE SOLUTIONS

This problem is part of an ongoing series of monthly puzzles developed in partnership with MoMath, an organization dedicated to engaging the public with mathematics. This collaboration highlights the puzzle's mathematical nature and its potential for broader appeal. Further details and insight into the solution are expected to be provided through future presentations.

Mentioned in This Episode

●People Referenced

Common Questions

In the game, you can select a bacterium. If the spaces directly above and to its right are empty, it can replicate, creating children in those spots and vacating its original position. The rule is one cell per point.