Vertical order on a ladder — who is at the bottom? Five boys A1, A2, A3, A4, A5 are on a ladder (top to bottom). A5 is above A1. A3 is under A2. A2 is under A1. A4 is above A3. Who is at the very bottom?

Introduction / Context:This is a partial-order (above/below) problem; we must deduce the lowest element consistent with all “above/under” relations.

Given Data / Assumptions:

• A5 above A1.
• A2 under A1 ⇒ A1 above A2.
• A3 under A2 ⇒ A2 above A3.
• A4 above A3.

Concept / Approach:From the chain A1 > A2 > A3 (where “>” = “above”), A3 is below both A1 and A2. Also A4 is above A3, and A5 is above A1. No statement puts anyone below A3.

Step-by-Step Solution:Combine: A5 > A1 > A2 > A3 and A4 > A3.Thus every named person (A1, A2, A4, A5) is above A3, while no one is stated to be under A3.Therefore A3 must be the bottommost.

Verification / Alternative check:Any attempt to place another boy below A3 contradicts at least one “under/above” relation.

Why Other Options Are Wrong:Each of A1/A2/A4/A5 is explicitly above someone else and hence cannot be the lowest.

Final Answer:A3