A riddle of ice and fire dragons - Henri Picciotto
It’s your first day in your new job
as Center Realm’s official cartographer,
and you've already got a big problem.
Center Realm is home to three
elder dragons: two ice, one fire,
and they’ve lived in harmony
on the east coast for centuries.
But scouts have sighted three fire dragons
and five ice dragons
flying across the Western Ocean.
You’ll only have a few hours to assign
them their designated regions
before they’ll arrive.
Elder dragons are extremely territorial.
Each must have its own,
officially acknowledged stomping ground.
They’ll peacefully roost there unless
their region borders another dragon
of the same type,
in which case the matching dragons
will go on a rampage.
However, fire and ice dragons
can border each other,
and matching regions can touch at corners.
You’ll soon have 11 dragons
and just 8 regions.
Fortunately, you have enough
political capital to create 3 new regions,
each of which must be
completely enclosed spaces.
Add more or otherwise mess this up,
and you’ll lose your job and your head.
Where do you draw lines
and place the new dragons?
Pause here to figure it out for yourself.
Answer in 3
Answer in 2
Answer in 1
It isn't difficult to create
three new regions.
What is more challenging
is to make sure the result
will keep each dragon
away from its own kind.
For instance, this can be
neither ice nor fire,
because it borders both.
However, create a new region like this,
and suddenly there are viable options.
Why did that work? Look at the point
where these four regions meet.
If you go around it, it alternates
between fire and ice.
Before the new line was added,
that wouldn’t have worked.
Nor would 5 or 7 regions.
6 and 8, however, both do.
The pattern is that points where lines
meet must be surrounded
by an even number of regions.
As long as that’s true, you can color
the map in two colors,
by alternating them around those points.
In our initial arrangement,
there were six such meeting points.
So what we want to do is connect
those to each other.
Each line adds a single new region
that touches both meeting points.
There are several ways to do this
to accommodate all 8 new dragons.
You’ve done such a great job
that your boss puts you in a ship
and sends you out across the Western Sea
to investigate
where these new dragons are coming from.
There you’re met
with a civilization in disarray.
Their 17 elder dragons are ravaging
the countryside, wiping out the peasants,
devastating all the people
and their thatch-roofed cottages.
And here there aren't just ice and fire
dragons, but lightning dragons too.
Their people will only allow
the creation of two new regions.
Where do you create new regions
and place all the dragons?
Pause here to figure it out for yourself.
Answer in 3
Answer in 2
Answer in 1
Unfortunately, our meeting-point trick
won’t suffice
now that there are three dragon types,
so we need to find another
method to identify problem areas.
A great way to do so is to experiment:
focus on one area and start coloring
until we run out of possibilities.
Take this section.
These 3 regions all border each other,
so they need to be different colors.
But they also all touch this giant
territory, which we now can’t color.
To generalize the issue, when there are
4 regions that all border each other,
it's impossible to color
them with three colors.
The map has two other such areas.
So what you need to do is break them up.
And once again, the key is drawing lines
between points
where multiple problematic regions touch.
No matter how you do it,
you’ll effectively subdivide
the giant territory into smaller ones.
Now coloring the map becomes
a logic puzzle.
So long as you approach it systematically
by starting in one area and radiating out,
you’ll reach an arrangement
that you can fit all your dragons into,
shifting the colors as needed.
Just assign this region last,
because it’ll have two options.
You've saved not one, but two continents
from certain ruin.
Now to see if you can find a giant eagle
and hitch a ride back home.
