As Lev and Kolya walk back across the bridge from Kamenny Island, Kolya insists that the colonel's daughter smiled at him, and questions who Lev's father is. Lev refuses to engage and calls Kolya a deserter. After some verbal sparring, the two continue walking. Kolya suggests trying to escape, but Lev insists they must find the eggs. Kolya says the Haymarket is their best chance, since it's primarily black market, and Lev concedes.
Kolya's belief that women are inherently attracted to him guides how he interacts with the opposite sex, and his friendly confidence is itself a kind of guarantor of his success. Lev, on the other hand, is envious and doubtful of this quality in Kolya and doesn't believe himself particularly worthy of admiration or attraction. This shows both Lev and Kolya's youth manifesting in different ways.
Lev thinks about the colonel's daughter skating naked, and Kolya seems aware of Lev's thoughts and teases him, saying "the secret to winning a woman is calculated neglect," which he says is a line from The Courtyard Hound. Kolya begins to describe the protagonist of the novel, Radchenko, and Lev says he sounds exactly like Oblomov (the protagonist from Ivan Goncharov's Oblomov), which irritates Kolya.
While Lev doesn't necessarily conduct himself as a romantic "catch" like Kolya does, he's not exempt from sexual fantasies either. Kolya's concept of calculated neglect provides a framework for interacting with women that involves manipulating them, which gives Kolya a great deal of power.
After a moment of silence, Kolya says that he was stationed at the fortress when the zoo was bombed. When Lev replies that he heard there were animals running around the city, Kolya says it's a nice story but they all died, including Betty the elephant, who took hours to pass away.
The Haymarket is six kilometers away, and Lev describes the city as they walk through it. Nevsky Prospekt is a ghost street now, but was once the heart of the city and a fine spot to watch pretty girls. Kolya cuts into Lev's thoughts, asking if he's a virgin. Lev asks Kolya why he cares, and Kolya replies that if they were friends, he could teach Lev things about girls, literature, and chess. They discuss betting on a game of chess, and Kolya suggests a bet of Lev's German knife against some pictures of French girls.
When it comes to sexual thoughts, Kolya appears to be a bit of a mind reader. This exchange does establish that Lev is a virgin, however, which sets up his maturation as something that will include sexual growth as well. Kolya asserts himself as a great teacher, and we see how highly Kolya thinks of himself.
Lev says he wasn't worried about losing the knife to Kolya because he already knew everyone in Piter who could beat him at chess. Lev was a young chess talent, but discovered as a teenager that he would never be truly great, and while quitting the club disappointed Lev's father, Lev enjoyed chess much more after he quit.
Lev’s chess prowess is established here, and that skill will prove critical later in the novel. Lev’s calmness in the face of Kolya’s chess challenge also suggests Lev’s potential for growth, as well as indicating that Kolya’s self-confidence can lead him to make mistakes.
Kolya points to a restaurant where he once took a girl, and begins to explain his theory of calculated neglect to Lev. He asks Lev if there's a girl he likes, and Lev suggests Vera. When Lev can't remember the color of Vera’s eyes, though, Kolya insists Lev doesn't really like her, and Lev is happy to follow instructions and forget Vera. Lev suggests the colonel's daughter, but it's decided that she's not for either of them.
While it was previously established that Lev is a virgin, in this exchange the novel establishes that his crush on Vera is a childish thing easily left behind, and foreshadows that he's likely to meet a woman he truly likes. And according to Kolya, his true interest in this woman will be obvious when he takes note of her eye color. Finally, though, their agreement that neither of them has a chance with the colonel’s daughter further marks how within the Soviet Union there are still class divisions that can’t be breached.
Lev and Kolya walk past young boys whitewashing over street signs and building numbers. Kolya accuses them of vandalizing the city, and is shocked by one boy's impertinence. As Kolya begins to argue with the boy, Lev interrupts that the boys are acting on orders, and if Fritz (a nickname for German soldiers) gets inside the city, they'll be lost without street signs. Kolya leaves the boy alone and declares the strategy "damn clever."
Amid the very normal idea of coming of age sexually, Lev and Kolya are confronted with the war. The war adds a sense of horror and absurdity to the lives it affects and colors the typical and mundane events of everyday existence. Lev’s recognition of the strategy also shows the value of his quick mind, while Kolya’s openness to Lev’s intelligence both shows their growing friendship and that Kolya’s self-confident bluster isn’t all there is to him.