Can You Solve the Lattice Bacteria Puzzle?
45sThe puzzle setup is instantly intriguing and challenges viewers to think, making them want to attempt it before seeing the answer.
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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.
Chapters
[00:01]
Replication Rule
A bacterium can replicate into the two spots above and to its right, but only if both are empty.
[00:27]
Puzzle Goal
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.
[00:41]
Collaboration and Follow-up
The puzzle is part of a monthly series with MoMath, and Peter Winkler will host a follow-up discussion.
Mentioned in this Video
Study Flashcards (3)
What is the rule for bacterium replication?
easy
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What is the rule for bacterium replication?
easy
Click to reveal answer
A bacterium can replicate into the two spots above and to its right, but only if both are empty.
00:01
What is the goal of the puzzle?
medium
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What is the goal of the puzzle?
medium
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To clear a 3x3 box with corners at (0,0), (0,3), (3,3), and (3,0).
00:27
Who is the mathematician hosting the puzzle?
easy
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Who is the mathematician hosting the puzzle?
easy
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Peter Winkler.
00:41
💡 Key Takeaways
⚖️
Replication Rule
The core mechanic of the puzzle is simple yet leads to complex combinatorial challenges.
00:01
📊
Puzzle Goal
The objective is clearly defined, making it a test of optimization and strategy.
00:27
💡
Collaboration with MoMath
The puzzle is part of a series, indicating a broader educational context.
00:41Full Transcript
[00:01] 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
[00:14] 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.
[00:27] >> 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
[00:41] 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
[00:55] [music] and I'll post my own video of the solution here sometime next month.
