Problem Setup and Conditions

This problem involves arranging five people—A, B, C, D, and E—on six numbered steps, starting from 1 at the bottom up to 6 at the top. The rules state that each step can hold at most one person. We are given specific relationships between the positions of some individuals:

• The step number where person A is standing is exactly two less than the step number where person C is standing. This can be written using LaTeX as: Step(A) = Step(C) - 2.
• The step number where person B is standing is one more than the step number where person D is standing. This can be written using LaTeX as: Step(B) = Step(D) + 1.

For this specific scenario, we are told:

• There are exactly two steps between the steps occupied by A and D.
• Person C is standing on Step 6.

Our goal is to determine the step number on which A is standing.

Determining A's Step

We know that person C is standing on Step 6.

Using the first condition provided, which relates A's position to C's position:

Step(A) = Step(C) - 2

Substitute the known position of C:

Step(A) = 6 - 2

Calculating this gives us:

Step(A) = 4

Therefore, based on the given information that C is on Step 6 and the rule Step(A) = Step(C) - 2, A must be standing on Step 4.

Verifying Other Conditions

Let's confirm this placement fits with the other conditions:

• Condition: Two steps between A and D. If A is on Step 4, the steps between A and D would be Step 3 and Step 2. This implies D must be on Step 1.
• Condition: Step(B) = Step(D) + 1. If D is on Step 1, then B must be on Step 1 + 1 = 2.

So, the positions derived are: D on Step 1, B on Step 2, A on Step 4, and C on Step 6. This leaves Steps 3 and 5 available for person E. All conditions are met consistently.

Conclusion on A's Position

Following the logical deductions based on the provided conditions, especially C's position on Step 6 and the relationship Step(A) = Step(C) - 2, we find that A is standing on Step 4.