Count Four-Digit Codes with Sum S

Problem Overview

• Count how many 4-digit codes (digits 0–9, leading zeros allowed) have a digit sum equal to S.
• Input: integer S in [0..36]; Output: the number of valid codes.
• Context: relevant to PIN/security code distributions and checksum-style constraints.
• Source: a Google interviews coding interview question; classic combinatorics problem.
• Ideal for practicing reasoning on an interview question with precise constraints.