Narrowing a January birthday using overlapping memories: Samant remembers his brother's birthday is after the 16th but before the 20th of January (i.e., 17th–19th). His sister remembers it is after the 17th but before the 19th (i.e., only 18th). On which date in January is the birthday?

Introduction / Context:
This is a precise intersection of two strict ranges on dates. The aim is to reduce a range of three possibilities to one by applying a tighter second constraint.

Given Data / Assumptions:

• Samant: after 16th and before 20th ⇒ {17, 18, 19}.
• Sister: after 17th and before 19th ⇒ {18}.
• All dates are in January of the same year.

Concept / Approach:
Translate verbal statements into sets and intersect them. Strict “after/before” excludes endpoints.

Step-by-Step Solution:

Verification / Alternative check:
Any misread (e.g., including 17 in the sister's set) would change the intersection; the strict phrasing prevents that.

Why Other Options Are Wrong:

• 17th/19th/16th/20th: Each violates one of the two strict windows.

Common Pitfalls:
Misinterpreting “before” as inclusive or forgetting that 20th is excluded.

Final Answer:
18th