Can you solve the multiverse rescue mission riddle? - Dan Finkel

It was a normal Tuesday
at the superconductor,

until a bug in the system created
a small situation.

Now your team is trapped in eleven
separate pocket dimensions.

Luckily for you, there’s a half-finished
experimental teleportation robot

that may be able to get you all home,

if you can figure out how to work through
the quirks of its design.

Over interdimensional radio,

your engineers explain that the robot
can teleport

into the alternate universes
you’re trapped in,

but it’ll do so completely at random.

The robot has two levers
and one big button.

When it appears,

you just switch the position of one
of the levers from A to B or vice versa,

and then the robot will note your
dimensional position

and teleport to another of the eleven
dimensions at random.

If it shows up again, you’ll have to pull
a lever before it’ll teleport away.

When anyone presses the button,

the robot will bring everyone who pulled
a lever back home.

Anyone who didn’t will be lost
in the multi-verse forever.

The challenge is to make sure everyone
has pulled a lever

before anyone hits the button.

While you can talk to each other now
over the interdimensional radio

and agree on a plan,

the robot’s teleportation technology

will interfere with all attempts
at communication once it arrives.

You won’t be able to attach messages
to the robot or scratch notes

into its superstrong alloy body.

Your only way to communicate information
is to change the position

of exactly one lever or hit the button.

What plan will make sure
everyone gets home?

It would be nice if you could set
different combinations of the levers

to indicate who’s already
been visited by the robot.

But it has only two levers.

That gives four combinations—

far too few to communicate
about 11 people,

especially when you’re forced to flip
one to send the robot onward.

There must be another way.

The critical insight is that

not everyone has to know when every pocket
dimension has been visited.

If one person accepts responsibility
ahead of time for hitting the button,

then only they need to know who the robot
has visited.

In fact, they don’t even need to know
exactly who’s been visited…

just how many people have been.

You volunteer to be the person in charge
of pressing the button

when the moment is right,

and give the following directions
to everyone else.

Your plan is simple:

you’ll use the left lever to count visits,

and the right lever will have no meaning,

so there’s no harm in
moving it up or down.

Each of the others will pull the left
lever

from position A to position
B exactly once.

If the robot appears with the left lever
already pulled down,

or if an individual has previously pulled
the left lever down

at any point in the past,

then they should move the right lever.

You, meanwhile, will be the only one who
ever resets the left lever from position B

to position A.

This gives you a way to count how many
people have been visited by the robot.

Everyone needs to pull the left lever
down exactly once,

and you’re the only one
to pull it back up.

So you know that the tenth time
the robot visits you

with its left lever in the down position,

it must have visited
all ten of the others.

And that means you’re safe to press the
button and teleport everyone home.

It may take a while–

most likely the robot will need to
teleport around 355 times;

but better that than leave anyone behind.

Your teammates phase back into your home
dimension one at a time.

The mission proves a great success.

Well...mostly.