This may seem unlikely since your customer remembers reading a short story, but I believe she has described a scene from Robert Sheckley's 1966 novel Mindswap. A shorter version was published as a novella, also titled "Mindswap", in Galaxy Magazine, June 1965, available at the Internet Archive. Please direct your customer's attention to chapters 19–21 of the novel, or chapters XVIII–XX of the novella, starting at this Internet Archive link.
After a series of adventures, the protagonist, Marvin Flynn, finds himself on the planet Celsus V. He has just met a character named Juan Valdez, who is going to help Marvin find his lost love, Cathy.
"Then you know nothing whatsoever about Cathy?"
"Only the little I have heard from you, which, frankly, amounts to practically nothing."
"Then how," Marvin asked, "can you possibly take me to where she will be?"
"It is simple enough," Valdez said. "A moment's reflection should clear the matter for you."
Marvin reflected for several moments, but the matter stayed refractory.
"Consider it logically," Valdez said. "What is my problem? To find Cathy. What do I know about Cathy? Nothing."
"That doesn't sound so good," Marvin said.
"But it is only half of the problem. Granted that I know nothing about Cathy, what do I know about Finding?"
"What?" Marvin asked.
"It happens that I know everything about Finding," Valdez said triumphantly, gesturing with his graceful terracotta hands. "For it happens that I am an expert in the Theory of Searches!"
"The what?" Marvin asked.
"The Theory of Searches!" Valdez said, a little less triumphantly.
"I see," Marvin said, unimpressed. "Well . . . that's great, and I'm sure it's a very good theory. But if you don't know anything about Cathy, I don't see how any theory will help."
Valdez sighed, not unpleasantly, and touched his mustache with a puce-colored hand. "My friend, if you knew all about Cathy—her habits, friends, desires, dislikes, hopes, fears, dreams, intentions, and the like—do you think you would be able to find her?"
"I'm sure I could," Marvin said.
"Even without knowing the Theory of Searches?"
"Well then," Valdez said, "apply that same reasoning to the reverse condition. I know all there is to know about the Theory of Searches, and therefore I need to know nothing about Cathy."
[. . . .]
"So what do we do?"
"I have just told you!" Valdez cried. "One must search, the other must wait. Since we have no control over Cathy's actions, we assume that she is following her instincts and looking for you. Therefore you must fight down your instincts and wait, thereby allowing her to find you."
"All I do is wait?"
"And you really think she'll find me?"
"I would stake my life on it."
"Well . . . all right. But in that case, where are we going now?"
"To a place where you will wait. Technically, it is called a Location-Point."
Marvin looked confused, so Valdez explained further. "Mathematically, all places are of equal potential insofar as the chances of her finding you are concerned. Therefore we are able to choose an arbitrary Location-Point."
"What Location-Point have you chosen?" Marvin asked.
"Since it made no real difference," Valdez said, "I selected the village of Montana Verde de los Tres Picos, in Adelante Province, in the country of Lombrobia."
"That's your home town, isn't it?" Marvin asked.
"As a matter of fact, it is," Valdez said, mildly surprised and amused. "That, I suppose, is why it came so quickly to my mind."
[. . . .]
Marvin bowed to the mustached man's superior wisdom and made himself at home in the posada. He settled himself at an outdoor table that commanded a good view of the courtyard and of the road beyond it. He fortified himself with a flagon of wine, and proceeded to fulfil his theoretical function as called for by the Theory of Searches: viz. he waited.
Within the hour, Marvin beheld a tiny dark figure moving slowly along the gleaming white expanse of the road. Closer it came, the figure of a man no longer young, his back bent beneath the weight of a heavy cylindrical object. At last the man raised his haggard head and stared directly into Marvin's eyes.
"Uncle Max!" Marvin cried.
"Why, hello, Marvin," Uncle Max replied. "Would you mind pouring me a glass of wine? This is a very dusty road."
Marvin poured the glass of wine, scarcely believing the testimony of his senses; for Uncle Max had unaccountably disappeared some ten years ago. He had last been seen playing golf at the Fairhaven Country Club.
"What happened to you?" Marvin asked.
"I stumbled into a time warp on the twelfth hole," Uncle Max said. "If you ever get back to Earth, Marvin, you might speak to the club manager about it. I have never been a complainer; but it seems to me that the greens committee ought to know about this, and possibly build a small fence or other enclosing structure. I do not care so much for myself, but it might cause a nasty scandal if a child fell in."
After a while Marvin's mother turns up at the Location-Point, and then his father, and finally Cathy. No lost socks, though.