Boxes Puzzle: Analyzing the Arrangement
The problem asks us to determine the number of boxes situated between box P and box G, given a set of clues about the stacking order of $7$ boxes (F, G, H, M, N, O, P).
Deducing Box Positions
We will deduce the order from top (position 1) to bottom (position 7) using the provided clues.
Position of O
Clue: "Only $2$ boxes are kept below O."
This implies O must be at the 5th position. The positions below O are 6 and 7.
Current Stack: [_, _, _, _, O, _, _]
Position of N
Clue: "Only one box is kept above N."
This means N is at the 2nd position. Position 1 is above N.
Current Stack: [_, N, _, _, O, _, _]
Position of H
Clue: "Only one box is kept between N and H."
With N at position 2, the only possible position for H to have exactly one box between them is position 4 (with position 3 being the box in between).
Current Stack: [_, N, _, H, O, _, _]
Placement of G and M
Clue: "G is kept immediately above M."
The pair 'GM' needs two consecutive empty slots. Checking the available slots: positions 1, 3, 6, 7 are empty. The only consecutive pair is (6, 7).
Therefore, G is at position 6, and M is at position 7.
Current Stack: [_, N, _, H, O, G, M]
Placement of P and F
Clue: "F is kept at some place below P."
The remaining positions are 1 and 3. The remaining boxes are P and F. To satisfy the condition that F is below P, P must be placed at position 1, and F at position 3.
Final Arrangement
The complete order of boxes from top (1) to bottom (7) is:
- P
- N
- F
- H
- O
- G
- M
Counting Boxes Between P and G
We need to find the number of boxes between P (position 1) and G (position 6).
The boxes located between P and G are N, F, H, and O.
The count is $4$.
Therefore, there are 4 boxes kept between P and G.
Important Questions from Box Puzzle
Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order. Only four boxes are kept between C and F. Only A is kept above C. Only two boxes are kept between D and E. G is kept immediately above B. E is not kept immediately above G. How many boxes are kept above G?
Seven boxes F, G, H, I, K, L, and O are kept one over the other but not necessarily in the same order. Only three boxes are kept below H. Only two boxes are kept between H and O. Only L is kept above G. F is kept at some place below I and at some place above K. Which box is kept at second position from the bottom?
- Seven boxes A, B, C, D, E, F, and G are kept one over the other but not necessarily in the same order. Only four boxes are kept between A and E. Only G is kept above A. Only two boxes are kept between B and C. D is kept immediately above F. C is not kept immediately above D. How many boxes are kept above D?
- Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order. Only three boxes are kept above A. Only one box is kept between F and A. Only three boxes are kept between F and E. E is kept at some place above A. B is kept immediately below E. G is kept at one of the places above D. C is not kept immediately above or below F. How many boxes are kept above B?
- Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order. Only two boxes are kept between G and A. Only F is kept above B. No box is kept below A. E is kept at some place below C but at some place above D. How many boxes are kept between D and F?
