The housekeeper and the professor - By Yoko Ogawa Page 0,7

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, working for the Professor was relatively easy: a small house, no visitors or phone calls, and only light meals for one man who had little interest in food. At other jobs, I always had to do as much as possible in a short amount of time; but now I was delighted to have so much time to do a truly thorough job of cleaning, washing, and cooking. I learned to recognize when the Professor was beginning a new contest, and how to avoid disturbing him. I polished the kitchen table to my heart's content with a special varnish and patched the mattress on his bed. I even invented various ways to camouflage the carrots in his dinner.

The one thing about the job that was always a little tricky was understanding how the Professor's memory worked. According to the old woman, he remembered nothing after 1975; but I had no idea what yesterday meant to him or whether he could think ahead to tomorrow, or how much he suffered.

It was clear that he didn't remember me from one day to the next. The note clipped to his sleeve simply informed him that it was not our first meeting, but it could not bring back the memory of the time we had spent together.

When I went out shopping, I tried to return home within an hour and twenty minutes. As befit a mathematician, the device in his brain that measured those eighty minutes was more precise than any clock. If an hour and eighteen minutes had passed from the time I walked out the door to the time I