The Red Blazer Girls (15 page)

Margaret maintains her composure. “It's all about the fly.”

“What fly?” Leigh Ann asks.

“The fly on the
ceiling
.”

We all look up.

“There's not a fly on the ceiling
now
, you imbeciles. The fly was on the ceiling in René Descartes's room.”

“Who? Who? Who?” we ask.

Flies, owls—what other creatures were in there with us?

“Come on. Sophie, you're French—you must know who Descartes is.
Cogito ergo sum
. Ring any bells?”

“The name does sound familiar,” I admit, “but I don't know anything about a fly. And that other thing you said—just tell us, okay? In English, please.”

“Yes, please,” Rebecca says. “I only speak English, Cantonese, a little Spanish, and text-messaging.”

“It's Latin for ‘I think, therefore I am.’ Descartes was a philosopher as well as a mathematician. He
invented
the coordinate plane. The story goes that one day he was lying in bed staring at a fly on the ceiling and became obsessed with being able to describe the motion of the fly as it walked around.”

Jeez, when I'm staring at the ceiling, I'm usually trying to figure out the lyrics to a song, or whether I should start plucking my eyebrows and how much it's going to hurt—it never involves higher mathematics or philosophy.

Rebecca raises her hand. “Um, Margaret? Can we get back to Zoltan's question? What the
hell
does this have to do with this ring of power we're trying to find?”

Margaret laughs. “The letter. Caroline's grandfather was telling her, in his way, that to solve the puzzle she needed to use the coordinate plane. Listen to what he says at the end of the letter:
‘sometimes in life the most difficult problems are solved by lying in bed and staring at that seemingly insignificant fly on the ceiling.’”

My eyes dart back and forth from Margaret to the whiteboard. “It's like a treasure map!”

“Basically. The clues are leading us to points on the floor of the church. The lines between the floor tiles make up a
perfect
coordinate plane. I'll show you.”

She turns back to the whiteboard and takes marker in hand. “This part is a little harder to explain, but trust me, it's not that hard, and once you see what I'm doing, well, you'll see—this whole puzzle is not nearly as difficult as we thought. Once I realized that the puzzle had something to do with the coordinate plane, I knew I was going to need Mr. Kessel's help. I remembered from math camp last summer that there was something about equations and graphing, but I couldn't remember how to do it. So, while you were off at your guitar lesson, I sent
Mr. Kessel an e-mail. I figured, what's he going to be doing on a Saturday afternoon? He doesn't strike me as the college football type. Probably online, right?”

“What
does
Mr. Kessel do on the weekends?” Rebecca asks. “Hang out with other math geeks, solving equations or something?”

I nudge her. “Hey, Rebecca—shhhhhhhh. Look around you. What
are you
doing?”

“Well, I must have been right about him being online because he wrote back to me in under ten minutes, and he sent me a link to a site that explained it all. I suppose I could just show you guys the site, but this is more fun, and I think I can explain it better.”

“Did Kessel ask why you wanted to know?” Rebecca seems skeptical that a teacher might be willing to help us out without some shady ulterior motive.

“Yeah, he was super-nice. I told him I was working on a math puzzle. He said to e-mail him if I got stuck and he'd help me out. He's not as bad as you guys think. He's funny!”

Leigh Ann agrees with Margaret. “I heard that he used to do stand-up comedy.”

“Mr. Kessel?” Rebecca asks. “He always looks at me like he's disappointed or something. Just because I'm Asian, everybody thinks I should be good at math.”

“Everyone does
not
think that, Becca,” I say.

“Asians are good at math?” Leigh Ann asks.

Point made.

Margaret continues with her lesson. “It's not just individual points like these that you can graph out on the coordinate plane, you can also graph
lines
and
equations
. For example, let's take a very simple equation.” She writes X + Y = 4 on the board and then draws two columns, one labeled X and the other Y. “Sophie, pick a number for X. Any number.”

“Two.”

“Okay Rebecca, if X is two, what does
Y have
to be in order to make this equation true? In other words, two plus
what
equals four?”

“Two?”

“Right! So there's one point. If X is two and Y is two, our pair is …” She wrote a two in the X column and a 2 in the Y column. “Now, give me a couple more numbers for X.”

“Three and six,” I volunteer.

“Good. If X is three, Y must be one, right?” She adds those numbers to the columns. “You
have
to make the equation true, so X plus Y
always
has to equal four. How about for six? What do you add to six to get four?”

“You can't,” says Rebecca. “You have to subtract. No, wait, that's wrong. You can add a
negative
number. Same thing. Six plus negative two equals four.”

“Exactly! So, now we have three pairs of numbers.” The whiteboard looks like this:

“Now watch what happens when we plot those points on our coordinate plane.” She quickly marks our three points in red. Then she places a yardstick against the whiteboard so that it hits all three dots and draws a line.

“This
line
now represents the equation X plus Y equals four. Pretty cool, huh? And you see, no matter what numbers you use for X and Y, as long as they make the equation true, those
points
will always fall right on this line.”

“I see that,” Rebecca says. “This
is
cool.”

“I know,” Margaret agrees. “But wait, it gets better. The next step is when you have
two
equations, which is what we just
happen
to have in this
letter. We'll get to our equation, the first one, anyway, in a minute, but let's do another example, to show you what happens when you have two equations.” On the side of the board she writes another equation, X − Y = 0, and the two columns that she again labels X and Y.

“When you have two equations, it's called a
system of equations
, and you can solve the system the same way we just graphed the first equation. When you're done, you're always going to have one of three things. One, the two equations will have exactly the same solution. In other words, they're the same line. We're not going to worry about that option. Second, you can end up with two lines that are perfectly parallel. We don't care about that one, either. The third one is the big one for us. It's when the two lines
intersect
. Let me show you, using this equation.”

In the X column she writes 2, 0, and 4, and then writes the same numbers in the Y column. “Are you with me? If X minus Y equals 0, then X and Y are always going to be the same, right? Now we graph these points and draw the line for that equation.”

“See, the line for this equation intersects the line for our first equation at this
one
point. This point, (2,2), is the
solution
to this system of equations. It is the
only
point that occurs on both lines.” For emphasis, she draws over the two lines several times, making a distinct X. “Now, do you remember what Raf said?”

“X marks the spot,” I say. “I think I've seen this in a movie.”

“I understand all this stuff,” says Leigh Ann, “but
I'm still not getting what it has to do with the actual
finding
of anything.”

“That's because you weren't in the church with us today,” said Margaret. “Remember, Soph, I told you how easy it was for me to figure out distances in the church because of those nice, neat twelve-inch floor tiles that are everywhere? The church
floor
is the coordinate plane. Get it? The way I see it, the nave and the choir are the Y-axis, and the transept is the X-axis. I suppose they could be aligned another way, but in the church it seems logical to be facing the altar. And remember, there is that thin strip of metal that runs right up the center of the aisle and another that crosses the church right in front of the altar table, right where the floor is raised up. The place where the metal strips intersect is our zero point, and the ring is somewhere
under
that floor. I'm sure of it.”

Margaret then erases everything on the board except the X-axis and the Y-axis. To one side, she writes the equation X + 3Y = 6 and then steps back. “Okay, Sophie, this one's all yours. This is what we have so far—the answers from the first three clues. Plot the line for that equation.”

I am suddenly very tingly “You mean that's it? All I have to do is draw the line that fits this equation, and we'll know where the ring is?”

“It's not quite
that
easy, Soph. Yes, we will know that the hiding place is somewhere on the line, but we won't know
where
on the line, which could be ninety feet long. And even if some of the tiles are loose, most of them probably aren't, and I doubt that Father Danahey would appreciate us digging up the entire church floor.”

“Oooohhhhh, now I get it,” says Rebecca. “We need to fill in the blanks in the
other
equation and then figure out where the line for
that
equation crosses the line for
this
equation. This is totally cool. I'm so getting into this. C'mon, what's the next clue?”

“Not until Sophie solves this equation,” Margaret says. “Come on, Soph. Find the Xs and Ys that will make the equation true, and then draw the line.”

I take the red marker in hand and write across the top of the board: