The mathematical centerpiece of Buck Privates is a word problem reminiscent of those spoofed by John Scieszka and Lane Smith in the delightful book Math Curse.

Abbott: You're 40 years old, and you're in love with a little girl, say 10 years old. You're four times as old as that girl. You couldn't marry that girl, could you?

Costello: No. ?

Abbott: So you wait 5 years. Now the little girl is 15, and you're 45. You're only three times as old as that girl. So you wait 15 years more. Now the little girl is 30, and you're 60. You're only twice as old as that little girl. ?

Costello: She's catching up. ?

Abbott: Here's the question. How long do you have to wait before you and that little girl are the same age?

Costello: What kind of question is that? That's ridiculous. If I keep waiting for that girl, she'll pass me up. She'll wind up older than I am. Then she'll have to wait for me!

Fast-talking, inveterate con man Abbott had a sneaky way with numbers (aided by mangled logic), especially when they had dollar signs next to them. Here's another encounter from Buck Privates, one echoed in several later movies.

Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me. That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time. First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!

Abbott then entices Costello into a silly, double-or-nothing number game.

Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?

Toward the end of the movie, during a boxing match, Costello is knocked to the canvas, and the biased referee gives a quick count: 2, 4, 6, 8, 10.

Costello: What's this? 2, 4, 6, 8, 10? What happened to 1, 3, 5, 7, and 9?

Ref: I don't like them numbers. They're odd.