The Virus Riddle: How to Solve a Deadly Outbreak

Imagine this: a prehistoric virus, unearthed from the permafrost, now threatens to escape a breached lab. You're the last line of defense. Can you navigate the contaminated facility, destroy the virus in every room, and make it out alive? This isn't just a hypothetical scenario; it's a fascinating puzzle rooted in mathematical principles.

The Perilous Predicament

A sudden earthquake has struck your research lab, shattering vials containing a deadly prehistoric virus. The lab, a 4x4 grid of 16 rooms, is now a death trap. The virus has been released into every room except the entrance, located in the northwest corner. Your mission: enter each contaminated room, activate its self-destruct switch, and escape through the exit in the southeast corner before the vents open and unleash an airborne plague.

The Catch

The security system is on lockdown. Once you enter a contaminated room, you can't leave without activating the self-destruct switch. And once activated, you can never re-enter that room. Can you find a route that allows you to destroy the virus in every room and reach the exit?

The Hamiltonian Path Problem

This puzzle is closely related to the Hamiltonian path problem, named after the 19th-century Irish mathematician William Rowan Hamilton. The challenge is to find a path within a graph that visits every point exactly once.

• NP-Complete: This type of problem is classified as NP-complete, meaning that while any proposed solution can be easily verified, finding one is notoriously difficult, especially when the graph is large.
• No Reliable Formula: There's no known formula or shortcut for finding a Hamiltonian path or even determining if one exists.
• Computational Challenge: It's uncertain whether computers can reliably find such solutions.

The Twist

This puzzle adds a twist: you must start and end at specific points. However, a true Hamiltonian path, starting and ending in opposite corners, isn't possible in this scenario due to the grid's configuration.

The Checkerboard Analogy

Consider a checkerboard grid with an even number of squares on each side. Every path through it will alternate between black and white squares. In such a grid, opposite corners are always the same color. Therefore, a Hamiltonian path that starts on one corner would have to end on a square of the opposite color, making it impossible to start and end on opposite corners.

The Loophole: A Second Chance

Just when all hope seems lost, a crucial detail emerges. The entrance room was not initially contaminated. This means you can leave it once without activating the self-destruct switch and return to it after destroying either of the adjacent contaminated rooms.

The corner room may become contaminated when the airlock opens, but that's acceptable because you can destroy the entrance on your second visit.

This return trip opens up four possible successful routes, and a similar set of options exists if you destroy the other adjacent room first.

Victory!

By exploiting this loophole, you've successfully navigated the lab, destroyed the virus in every room, and prevented a potential global catastrophe. Your quick thinking and attention to detail saved the day!

Perhaps after this ordeal, a less stressful career as a traveling salesman might be in order.