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The good news is that your experimental robo-ants
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are a success!
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The bad news is that you accidentally
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just gave them the ability to shoot deadly lasers
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…and you can’t turn it off.
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You have five minutes to stop them
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before the lasers go online.
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Until then,
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all of your robo-ants will walk
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inside their habitat at a speed of
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exactly 1 meter per minute.
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If they bump into each other or hit a dead end,
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they’ll instantly turn around
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and walk back the way they came.
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When five minutes are up,
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they’ll turn on their lasers,
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break free,
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and stream out into the world,
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carving a path of destruction as they go.
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Your one chance to stop them is to insert
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the two emergency vacuum nozzles into the habitat
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and suck the ants up before they break free.
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The nozzles can press into any one location
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in the habitat through a membrane covering
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its front side, and any ants that walk past
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will be sucked up and deactivated.
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You can’t move the nozzles once they’re placed
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without leaving a hole that the robo-ants
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would pour out of, so choosing the
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right spots will be key.
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The habitat is made out of meter-long tubes.
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When the robots reach an intersection,
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they will pick randomly whether to go
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left, right, or forward.
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They only go backward if they hit
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hit another robo-ant or a dead end.
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Unfortunately, there are hundreds of them
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inside the habitat, and if even one escapes,
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it’ll do a lot of damage.
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With just less than five minutes remaining,
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where should you place the 2 vacuum nozzles
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to suck up all the robo-ants?
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Pause the video now if
you want to figure it out for yourself.
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Answer in: 3
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Answer in: 2
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Answer in: 1
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With robo-ants ricocheting all over the habitat,
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it might seem impossible to stop them
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before they break free.
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But this situation is simpler than it seems.
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Here's why.
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Imagine just two robo-ants crawling
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toward each other.
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When they collide, they immediately
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reverse directions.
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And what would that sequence of events look
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like if they crawled past each other instead?
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It would look exactly the same before
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and after their collision, but with
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their positions swapped.
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This is true every time a pair of robo-ants meet.
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Because the identities of individual ants
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don’t matter, you just need to figure out where
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you should put the nozzles to capture
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any single ant walking without interruption
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for less than 5 minutes, starting from
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any point in the habitat.
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That’s much easier to conceptualize and solve.
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Placing the nozzles at intersections where
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three or four tubes meet seems like your best bet
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since that’s where the robo-ants might otherwise
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change directions and miss your nozzles.
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There are only four intersections…
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which two should you pick?
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The top right intersection has to be one of them.
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If it isn’t, an ant crawling down from
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this intersection toward the dead end would
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crawl for four minutes to get back to the
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intersection, and then go in any of three
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directions, walking for at least another minute.
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Once you’ve placed a nozzle in the top right,
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the only other choice that has a chance
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to work is the bottom left.
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To see that this works, imagine an ant
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anywhere else in the habitat.
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Worst case scenario, the ant would start
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right next to the vacuum nozzle, marching away from it.
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But in all those worst cases, the ant would march
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for at most 4 meters before being sucked
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up into the vacuum.
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No other choice of two intersection points
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is guaranteed to get all the robo-ants
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within five minutes.
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Having vacuumed them all up, you’ve
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averted a major crisis.
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Before you mess with robo-ants again,
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you’ll want to have a robo-anteater ready.
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And wouldn’t it be cool if it could
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fly and breathe fire?
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There’s no way that could go wrong!
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