The Killer Robo-Ants Riddle: Can You Solve It?

Imagine a scenario: your experimental robo-ants are a success, but with an unforeseen and dangerous upgrade – the ability to shoot deadly lasers that you can't disable. With only five minutes before these lasers activate, threatening widespread destruction, your mission is to contain them. How do you prevent their escape?

The Robo-Ant Challenge

These robo-ants move at a consistent pace of 1 meter per minute within their habitat. When they collide with each other or reach a dead end, they instantly reverse direction. Your only recourse is to strategically place two emergency vacuum nozzles inside the habitat to suck up and deactivate the ants before their lasers come online.

The nozzles are stationary once placed, and the habitat consists of meter-long tubes. At each intersection, the robo-ants randomly choose to go left, right, or forward, only turning back upon encountering an obstacle. With hundreds of ants in the habitat, even a single escapee could spell disaster.

Given these constraints, where should you position the two vacuum nozzles to ensure the capture of all robo-ants before time runs out?

Decoding the Solution

The seemingly chaotic movement of the robo-ants simplifies upon closer inspection. Consider two ants moving towards each other. Upon collision, they reverse direction. However, the outcome is identical if they simply passed through each other, swapping positions.

This principle applies to every encounter between robo-ants. Since individual identities are irrelevant, the challenge boils down to identifying locations that can capture any ant walking uninterrupted for less than five minutes from any point within the habitat. This reframing makes the problem significantly more manageable.

Strategic Nozzle Placement

Positioning the nozzles at intersections where three or four tubes converge appears to be the optimal strategy. These locations maximize the chances of capturing ants that might otherwise change direction and evade the nozzles.

Given the habitat's layout, the top right intersection must be one of the chosen locations. Otherwise, an ant crawling down from this intersection towards the dead end would travel for four minutes before returning to the intersection. It could then move in any of three directions, adding at least another minute to its journey.

With one nozzle placed in the top right, the bottom left intersection emerges as the most viable second choice. To understand why this works, consider an ant located anywhere else in the habitat. In the worst-case scenario, the ant begins its march directly away from the nearest vacuum nozzle.

However, even in these worst-case scenarios, the ant will travel a maximum of 4 meters before being sucked into a vacuum nozzle. No other combination of two intersection points guarantees the capture of all robo-ants within the five-minute time limit.

A Crisis Averted

By strategically placing the vacuum nozzles, you successfully contained the robo-ants, averting a potential catastrophe. Perhaps, before experimenting with robo-ants again, a robo-anteater with the ability to fly and breathe fire might be a worthwhile investment – what could possibly go wrong?

Italicized text indicates key concepts and strategic elements in solving the riddle.

• Robo-Ant Behavior: Understanding their movement patterns is crucial.
• Strategic Placement: Nozzle positioning is key to success.
• Worst-Case Scenarios: Planning for the most challenging situations ensures complete capture.