Can you solve the time traveling car riddle? - Dan Finkel
Your time traveling has caused a few
issues with the space-time continuum,
like your old high school bully, Riff,
now ruling the future with an iron fist.
You and the professor have driven
your hovering DeLorean back to the past
to undo your own meddling.
But shortly after you fix your mistakes,
another DeLorean appears
and crashes into yours.
Out step older versions
of you and the professor,
who apparently had the same idea
from somewhere else in the timeline.
The professors panic and explain
that the universe could collapse
now that you’re both
in the same time and place.
The only hope is to merge the time streams
by having each version of you
simultaneously time travel home.
You both have plenty of fuel,
but the crash broke your
chrono-stabilizing gyroscopes
and your cars can only time travel
under very specific circumstances.
Each of you will need to drive
a mile south, then a mile east,
and then a mile north to get
the gyroscopes into temporal alignment.
That would be easy,
except each calibration requires placing
a portable time gate
at your starting point,
then driving into it at the precise end of
your three mile drive without it moving.
Not only that, but your two time gates
must be placed at least 100 miles apart
so their signals don’t interfere.
In other words, you need to find two
different locations where you can drive
a mile south, a mile east,
and then a mile north
and end up exactly where you started.
The professors are about to show you where
you can do this when they vanish,
becoming victims
of the collapsing timeline.
It’s up to you now:
where can you place the time gates?
Pause here to figure it out yourself.
Answer in 3
Answer in 2
Answer in 1
If the earth were flat, there would
be no way to solve this riddle.
What you need is some way to use the
sphericalness of the planet,
some of its notable features,
and the fact that lines of latitude aren’t
really lines— they’re circles.
The equator is the biggest of these
circles, but it doesn’t do much for you,
and you can’t even go south
from the South Pole.
But let's try the North Pole.
When you go a mile south, you'll be
on a circle that runs east west.
After a mile east, you’re still
on that same circle,
so the final mile north brings you
back to your starting point.
Perfect.
That’s one gate down, but where
should you place the second?
Well, the nice thing about circles is
that if you travel on them far enough,
you come back to where you started.
If there were a circle that had
a circumference of one mile,
that would work marvelously.
You could drive south a mile to reach it,
make the one mile rotation east,
then go north a mile to return
to where you started.
Such a circle does exist just
north of the South Pole.
To find your starting point,
you can use the standard formula
for the circumference of a circle.
If you wanted to be absolutely precise,
you could use an equation
that takes into account
the roughly spherical shape of the Earth.
But an area this small is
so close to being flat
that the standard formula gives a solution
within a fraction of an inch
of the actual distance.
A circle with a one mile circumference has
a radius of just under 0.16 miles,
so any point on the circle
one mile north of that
will be suitable for your time gate.
In fact, there are other answers too:
start a little further south,
and you could travel east around the
Earth twice, three times, or more!
In theory, there are infinite
possible starting points,
but the circles get so tight that they
aren't actually practical to drive.
Everything’s getting a little weird
by the time you reach
your starting points.
You drop the time gates,
sync up with your doppelgänger,
and slam down the pedal.
You both reach 88mph just as you complete
your three mile circuits,
merge the timelines,
and save the universe.
