The housekeeper and the professor Read Online Free

themselves. Like this."
    220 : 1 2 4 5 10 11 20 22 44 55 110
142 71 4 2 1 : 284
    The Professor's figures, rounded and slanting slightly to one
side, were surrounded by black smears where the pencil had
smudged.
    "Did you figure out all the factors in your head?" I asked.
    "I don't have to calculate them—they just come to me from the
same kind of intuition you used. So then, let's move on to the next
step," he said, adding symbols to the lists of factors.
    220 : 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 =
=142 + 71 + 4 + 2 + 1 : 284
    "Add them up," he said. "Take your time. There's no hurry."
    He handed me the pencil, and I did the calculation in the space
that was left on the advertisement. His tone was kind and full of
expectation, and it didn't seem as though he were testing me. On
the contrary, he made me feel as though I were on an important
mission, that I was the only one who could lead us out of this
puzzle and find the correct answer.
    I checked my calculations three times to be sure I hadn't made
a mistake. At some point, while we'd been talking, the sun had set
and night was falling. From time to time I heard water dripping
from the dishes I had left in the sink. The Professor stood close by,
watching me.
    "There," I said. "I'm done."
    220 : 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
    220 = 142 + 71 + 4 + 2 + 1 : 284
    "That's right! The sum of the factors of 220 is 284, and the sum
of the factors of 284 is 220. They're called 'amicable numbers,'
and they're extremely rare. Fermat and Descartes were only able
to find one pair each. They're linked to each other by some divine
scheme, and how incredible that your birthday and this number
on my watch should be just such a pair."
    We sat staring at the advertisement for a long time. With my
finger I traced the trail of numbers from the ones the Professor
had written to the ones I'd added, and they all seemed to flow together,
as if we'd been connecting up the constellations in the
night sky.

2
    That evening, after I'd got home and put my son to bed, I decided
to look for "amicable numbers" on my own. I wanted to see
whether they were really as rare as the Professor had said, and
since it was just a matter of writing out factors and adding them
up, I was sure I could do it, even though I'd never graduated from
high school.
    But I soon realized what I was up against. Following the Professor's
suggestion, I tried using my intuition to pick likely pairs,
but I had no luck. I stuck to even numbers at first, thinking the
factors would be easier to find, and I tried every pair between ten
and one hundred. Then I expanded my search to odd numbers,
and then to three-digit numbers as well, still to no effect. Far from
being amicable, the numbers seemed to turn their backs on each
other, and I couldn't find a pair with even the most tenuous
connection—let alone this wonderfully intimate one. The Professor
was right: my birthday and his watch had overcome great trials
and tribulations to meet each other in the vast sea of numbers.
    Soon, every inch of the paper was filled with figures. My method
was logical, if a little primitive—yet I ended up with nothing to
show for all my work.
    I did make one small discovery: the sum of the factors of 28
equals 28.
    28 : 1 + 2 + 4 + 7 + 14 = 28
    Though I wasn't sure this amounted to anything. None of the
other numbers I'd tried were the sum of their own factors, but
that didn't mean there weren't more out there. I knew it was an
exaggeration to call it a "discovery," but for me it was just that.
This one line of numbers stretched across the page as if pulled
taut by some mysterious intention.
    As I got into bed, I finally glanced at the clock. It had been
much more than eighty minutes since we'd had our talk about amicable
numbers. By now he'd have forgotten all about our secret,
and he'd have no idea where the number 220 had come from. I
found it difficult to fall asleep.
     
    From a housekeeper's perspective,