Education and Communications

Can You Solve The Giant Spider Riddle? – Dan Finkel

Once every century, the world’s greatest
spiders gather to compete in a series of grueling games. The winner will become
the next arachnomonarch, able to command all the world’s spiders
to their will. That day is today, and for the first time, you’re casting your name into the ring. From Anansi to Arachne to Aragog, all of the titans of the
spider world are here, and at first, no one even notices
itsy-bitsy you. But after wowing the crowd
with your web design and sticking it to the competition
in the long-distance sling, you’ve qualified for the finals. Now all that remains is to face off
against the reigning champion, Queen Shelob, on the Whirled Wide Web,
and win the title from her. The web stretches over a large chasm, with intersecting strands coming
to a single point on the other side. Moving across each strand
requires a careful dash, and you must keep going until
you stop at the next hub where two strands cross. By ancient spider code, only one
competitor may traverse the web at a time. You must take turns, moving from one
intersection to an adjacent one. No one may spin new paths
into existence or skip turns. You begin two spaces from Shelob,
and to win, you must catch her by your tenth move. Can you attain the mantle
of spider supremacy? Pause here to figure it out for yourself.
Answer in 3 Answer in 2 Answer in 1 It’s tempting to trap Shelob in a corner,
but doing so is surprisingly tricky. The layout of the web
is such that every move you make, Shelob can get to another intersection
two away from you. So even if you were to drive her
into a corner, she’d escape it easily. There are no dead ends, so there’s never a situation where she’d
be forced to move to your space. However, there is this point up here
where all the strands converge. It’s easy to see that it’s important, but the challenge is figuring out
exactly what to do with it. There’s a clever way of re-visualizing
the problem: try coloring every intersection
one of two colors— say red and blue— where the same color never borders itself. What you get is a checkerboard pattern, then one space at the point
which you can’t make either color. At the beginning of the game,
every time you move to red, Shelob will be on blue, and every time you move to blue,
Shelob will be on red. In other words, unless something changes, you can never move onto the same
intersection as her. And that’s where the point comes in. As indicated by its unique color, it’s the
one place you can break the pattern and change the rhythm of moves. So you should waste
no time in getting up there. Shelob could now be in any one
of these red spaces, and you have at most 6 moves
left to catch her. But thanks to the colors we’ve added, we can now focus on the one thing
that matters the most: changing the color pattern. Shelob is on red, so you should move
onto red on the second or fourth strand. Now, Shelob can never move to any
of the spots neighboring you, giving you a kind of net
to use to catch her. You may have luck choosing your moves
through intuition at this point. But if you want to get
algorithmic about it, you could track how far away she is
horizontally and vertically, as two numbers. On your move,
shrink the larger of the two, and no matter which direction she runs,
she’ll have to hit an edge. Eventually, you’ll have backed her
into one of the two corners and catch up to her
at the last possible moment. You snatch the ceremonial sash
from your opponent and wrap it around yourself. You are now the Spider Supreme, leader of all the world’s
eight-legged wonders. Just remember— with great spider power
comes great spider responsibility.
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