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