Solving the Logic Puzzle: Arrangement of Seven Boxes

This solution details how to solve the logic puzzle involving seven boxes stacked vertically.

Understanding the Constraints

We are given seven boxes: A, B, C, D, E, F, G. They are stacked one above the other. We need to find the number of boxes below box C based on these rules:

• Rule 1: Only A is kept above F. This means A is at a higher position than F (A > F).
• Rule 2: Only D is kept between F and C. This implies that D is directly between F and C, forming a sequence of three boxes: either F, D, C or C, D, F from top to bottom.
• Rule 3: Only E is kept below B. This means B is at a higher position than E (B > E).

Deriving the Arrangement

Let's analyze the possible arrangements based on the rules:

From Rule 2, we have two primary possibilities for the relative order of F, D, and C:

• Possibility 1: The sequence is F, D, C (top to bottom).
• Possibility 2: The sequence is C, D, F (top to bottom).

Now let's incorporate Rule 1 (A > F):

• If Possibility 1 (F, D, C) is true, then since A must be above F, the combined relative order must be A > F > D > C. This establishes the order for 4 boxes.
• If Possibility 2 (C, D, F) is true, then A must still be somewhere above F.

To arrive at a single answer, we consider the most constrained scenario that fits the constraints. The structure A > F > D > C provides a strong relative order.

Let's assume this relative order implies that A, F, D, C occupy the topmost positions available that satisfy the rules.

Consider the arrangement where A, F, D, C form the top four boxes of the stack:

1. Position 1 (Top): A
2. Position 2: F
3. Position 3: D
4. Position 4: C

This arrangement satisfies Rule 1 (A is above F) and Rule 2 (F, D, C sequence). The boxes A, F, D, C are placed, fulfilling their relative order.

The remaining positions (5, 6, 7) must be filled by the remaining boxes: B, E, and G.

Rule 3 states that B must be above E (B > E).

The boxes below C (which is at Position 4) are the boxes in positions 5, 6, and 7. These boxes are B, E, and G.

The constraint B > E only dictates the relative order of B and E among the boxes below C. Regardless of the specific order of B, E, and G in positions 5, 6, and 7 (e.g., B, E, G or B, G, E or G, B, E), all three boxes (B, E, and G) will be below C.

Determining Boxes Below C

In the derived stack configuration:

• Box C is at Position 4.
• The boxes located below Position 4 are in positions 5, 6, and 7.
• These positions are occupied by boxes B, E, and G.

Therefore, there are exactly 3 boxes kept below C.