Can you cheat death by solving this riddle? - Shravan S K
You and your best friend Bill are
the greatest bards in the kingdom—
but maybe not the brightest.
The hit song you performed
at last night’s fair insulted the king,
and now your hours are numbered.
Just before your execution,
you’re approached by the princess,
who happens to be a big fan.
She slips you a pouch containing
two magic, six-sided dice
that can land any way you wish.
You have no idea how this could possibly
help, but you thank her anyways.
As everything goes dark,
you both suddenly find yourself standing
in a deep cavern before a robed figure.
It turns out that Death is a connoisseur
of most excellent music.
He’s decided to give you a chance
to escape your fate
by beating him at his favorite game:
life-sized Snakes and Ladders.
The cavern has 100 rooms connected
by passageways
as well as— you guessed it—
snakes and ladders.
Each turn one of you will roll a die,
then advance that many rooms.
Ending your move at the bottom
of a ladder means moving up to the top,
while ending on a snake’s head
will make you slide down to its tail.
Each of you must make your way
through the cavern
and reach the exit in fewer turns
than Death himself.
Before you can think twice,
your host starts casting his die,
and within 6 rolls he’s reached
the cavern entrance.
“Better get moving,” he says.
“Oh, and by the way, once one
of you uses a snake or ladder,
it’ll disappear and be inaccessible
to the other.”
You have no idea how you can possibly
get lucky enough to win,
but then you remember your magic dice.
Can you figure out a sequence of rolls
that will get both of you to the exit
in 5 or fewer moves each?
Pause here to figure it out yourself.
Answer in 3
Answer in 2
Answer in 1
The cavern contains many
routes to the exit,
and it’s natural to gravitate
to the ladders
that allow you to cover a lot of ground,
quickly.
Like this one— on turn 2 you’d be at 75,
but without any further ladder boosts,
you’d need another 5 rolls to get out.
Or this one— three ladders get you to 82,
but then it would take another 4 rolls
to get around the pesky snake at 88.
In fact, there’s no path
that can get you to the exit
in 5 moves using exclusively ladders.
So where does that leave you?
Snakes.
It’s counterintuitive to make
moves that take you farther away
from your target,
but snakes open up a surprising amount
of opportunities.
For instance, these three ladders would
put you a single roll from the exit,
but cost too many turns
to reach by ladders.
These two are, however, only 5 and 12
rooms from snake tails, respectively.
So could you work backwards from those
to find a 5 roll path?
There are exactly two 5-turn routes
you might find using these ladders:
Ladder snake snake ladder exit,
and ladder ladder snake ladder exit.
So that’s it, right?
Unfortunately, no—
the two paths share a snake and a ladder,
each of which will be unusable after
the first of you slides and then climbs.
You won’t find 5-turn
moves anywhere else,
so is one of you doomed?
There’s one more possibility to consider:
the disappearing ladders and snakes
can impede your progress,
but could they also help it?
There are two paths to the 94 ladder
that almost work,
except for this snake,
at exactly the midpoint
between the two ladders.
If Bill were to take that snake
on his route,
you could then get past it
and up to the exit in just 5 moves.
And good news—
whichever path you choose,
one of the 5-roll paths we found
earlier does exactly that
without using any
of your snakes or ladders.
So all you need is for Bill to go first
and stick to the plan.
You and Bill both reach
the cavern entrance
and climb back into the public square,
to everyone’s surprise.
Before the guards can seize you again,
you wow the crowd— and king— with a song
about your epic contest with Death.
