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!