Can you solve the Trojan War riddle? - Dennis E. Shasha
The Trojan War has been raging
for 10 years,
with neither Greeks nor Trojans
prevailing.
Gods and humans alike
are desperate for a break,
so when a divine omen races
across the sky,
the two sides agree to a 10 day truce.
From high up on Olympus you’ve been
waiting for an opportunity
to bring this bloody war
to its conclusion.
When you go to consult the Fates,
they advise:
should the peace last for a full 10 days,
all will end soon.
However, if the truce is broken,
the ensuing battle will lead to 10 more
devastating years of war.
The Fates’ loom has shown them
the exact conditions
that will keep the truce intact.
The great Trojan plain can be viewed
as a grid of Greek and Trojan encampments.
If they’re organized in such a way that
any Greek can reach any other Greek camp
without having to pass through a Trojan
camp, and likewise for Trojans,
plus neither side completely surrounds
the other, peace will prevail.
Anyone can move to a horizontally
or vertically adjacent camp,
but never diagonally.
The problem is,
they’re currently arranged like this.
Tonight, you can use your powers to swap
up to six pairs of camps
that are horizontally, vertically,
or diagonally adjacent.
No camp can be moved more than once.
Which swaps do you make
to keep the peace?
Pause here to figure it out yourself.
Answer in 3
Answer in 2
Answer in 1
The first insight here is to divide
this into two sub-problems.
There’s the matter of connecting
4 clumps of Greeks
without putting holes in the Trojan line.
And then there’s dealing
with the thorny center space.
Let’s consider the Greeks first.
To connect any Greek clumps,
you’ll have to mess
with the nice, straight Trojan lines.
If you try to do that anywhere
in the center of these arms,
you'll create new isolated
clusters of Trojans.
So the only option is to go
to the perimeter of the field
and move some Trojans diagonally,
say here, here, and here.
Now for the center.
there’s no way to connect the Trojan arms
without swapping a Trojan in.
But continuing to shift that arm
of Trojans inward
would require moving
the same Greek camp multiple times.
However, you could shift the whole
Trojan arm up and to the right,
closing this gap.
There are several
solutions with slight variants,
but as long as you perform this maneuver
on the short arm of Trojans,
you can achieve peace in exactly 6 moves.
You make the swaps and all is well
until the fifth night.
One of your rival gods wants
to see the bloodshed continue,
and has taken advantage
of a forgotten prophecy.
He’s convinced one Trojan camp
to make a swap
with their horizontal, vertical,
or diagonal Greek neighbors
that will break up the Greek connectivity.
Once again, you consult the Fates,
who prophesize the following:
the meddling Trojan camp is somewhere
within four grid spaces
of the perimeter of the battlefield.
They won’t go through with a swap
if it only breaks up Trojan connectivity.
And finally, you can make
at most two swaps
with the same rules as before
to thwart them.
Which swaps do you make
to block the troublesome Trojan camp?
Answer in 3
Answer in 2
Answer in 1
You won't be able to identify
the scheming camp precisely,
but there’s a lot you can do
to at least narrow down the options.
They have to be somewhere in this area.
And they have to be able to block Greek
camps from each other in a single swap.
That doesn’t leave many options;
the only possible blockages
are at the end of these two arms,
where a Trojan camp could plug a hole
without opening a new one.
So they must be in one of these
four camps.
Let’s look at the right arm first.
There’s a threat here because this column
has two Trojan camps.
If one moves to the right,
the other will still be in place,
blocking Greeks from crossing.
so we can thwart them by moving either one
a column left into this square.
and the same principle applies
to the bottom arm.
Your effort maintains the peace
for the final 5 days.
But it seems that a certain Greek general
noticed what was happening
and left the Trojans a parting gift...
