Gautam Soundararajan
Math 7
4/3/13
My Favorite Puzzle
I have always been attracted to puzzles, whether they were word puzzles, math puzzles,
or even physical puzzles. Each puzzle is different and mysterious and has a secret waiting to be
discovered. Yet the majority of puzzles have no actual worth. The solution does not improve the
solver’s standard of living or help solve a complex problem facing the world. Puzzles are merely
a way to test intellect and persistence while providing a means of entertainment. Once I have
seen a puzzle, I cannot put it down. I will spend hours trying to determine the solution. Part of
the reason is that I like a challenge. If the puzzle is difficult to solve, but I eventually derive an
answer, I feel accomplished. I was able to solve a complex problem with my cleverness and
intelligence. This leads to the other reason why I enjoy puzzles. If I am able to solve a difficult
puzzle and other people are not, I feel better about myself. This may not be a good quality to
have, but it is true of me nonetheless. I feel more intelligent than others around me. It is not that I
enjoy degrading others, but rather that I enjoy being recognized for my achievement.
Several years ago, when I was in middle school, my father brought my brother and me
together and gave us a puzzle to work on. The puzzle related to math - my favorite subject in
school. At that age, I found the puzzle to be tricky. I had to work on it for quite some time before
eventually solving it. Looking at the puzzle now, I could probably determine the solution in a
matter of minutes if I had not already seen it. After all, I have become more perceptive and
clever from many years of schooling. The answer to the puzzle was not memorable. The process
of finding the answer was. In addition, disproving my father’s belief that I would not be able to
solve the puzzle made the experience even more gratifying. It was not that I was disproving my
father, but rather that I was disproving his notion of my intelligence. I was also able to solve the
problem while my brother could not. My brother is two years younger so it is reasonable to
assume that I would be able to solve it and he would not or that I would solve it sooner than he
would. Solving the puzzle first reaffirmed my notion that I was more intelligent than he was
since I was older than him.
My father told the puzzle one way, with a specific story behind it. I frame the puzzle in a
different context. The question is still the same in both cases, but my scenario is more interesting
than my father’s to people my age. Now, to the actual puzzle.
Gandalf the Grey, using his wizardly powers, has recently determined that the Fellowship
is being hunted by the Balrog of Moria. The group, consisting of Legolas, Aragorn, Frodo, and
Sam, must cross the Bridge of Khazad Dum before the Balrog kills them. The other members of
the Fellowship have already crossed the bridge. However, the group is faced with a predicament.
Gandalf is fighting the Balrog on one side of the bridge. Yet he can only hold off the beast for 17
minutes. - Don’t ask how he came up with this time. Gandalf is a wizard and his powers are
beyond simple humans. - On the other side of the bridge, the other members of the Fellowship
are fighting off a horde of orcs. By coincidence, it will take them exactly 17 minutes to
exterminate the orcs. Only when the entire group is on the other side of the bridge will the orcs
notice them and kill them. This means Legolas, Aragorn, Frodo, and Sam must cross the bridge
in exactly 17 minutes. Legolas, being a nimble elf, can sprint across the bridge in one minute.
Aragorn, a ranger, takes slightly longer: two minutes. The two hobbits, Frodo and Sam, take the
longest time to cross the bridge since their legs are too short. Sam, being the porkier of the two,
takes ten minutes to cross, while Frodo takes five. But the bridge can only hold two of the group
at a time without cracking. It is also dark. To combat the darkness, the Light of Earendil is used
by the group. In order to cross the bridge, somebody must be holding the Light. How will the
four of them cross the bridge, ensuring that all of them survive?
The solution seems straightforward. But the various conditions make it more difficult to
determine the answer. In order to ensure the survival of the group, Legolas and Aragorn must
cross the bridge first, taking two minutes. Then Aragorn goes back with the Light. They are at
four minutes. Frodo and Sam cross next. The overall time is now 14 minutes. Legolas takes the
Light and runs back across, with 15 minutes on the clock. Legolas and Aragorn cross the bridge
a final time and the total time is now 17 minutes. The group was able to escape the Balrog and
avoid death by the orcs. Another possible solution is to let Legolas take the Light back in the
second step.
The reasoning behind it is rather simple. Frodo and Sam must cross the bridge the least
number of times possible since they take the longest. Thus, they cross once by going together.
But Legolas and Aragorn must cross before them so there is somebody to return the Light. With
this in mind, the solution is straightforward.
This puzzle is enthralling and tricky. It has everything that a good puzzle should have.
For these reasons, I consider it my favorite puzzle.