Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order. Only A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
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:
- Position 1 (Top): A
- Position 2: F
- Position 3: D
- 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.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
Who is sitting exactly in the middle ? Seven people, C, D, E, F, L, M and N, are sitting in a row, facing north.
Only two people sit to the right of C. Only two people sit between C and L. Only two people sit between E and N. N sits to the immediate left of C. M sits to the immediate right of F. Who sits at the third position from the left end of the row?- Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. Only three people sit between E and D. A sits to the immediate left of D. No one sits to the right of B. Only two people sit between B and A. G sits to the immediate right of F. How many people sit to the right of F?
P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
A, B, C, D, J, K and L are sitting around a circular table facing the centre of the table. K sits to the immediate right of B. Only three people sit between K and A when counted from the left of K. Only three people sit between B and L. C sits to the immediate right of D. How many people sit between J and D when counted from the left of D?
