Analyzing the Box Arrangement Logic Puzzle

This problem requires us to determine the order of seven boxes stacked vertically based on a set of given conditions and then identify the box at the bottom.

Step-by-Step Deduction

Let's represent the positions from top to bottom as 1, 2, 3, 4, 5, 6, 7.

• Condition 1: "Only three boxes are kept above G." This means G must be in the 4th position.

  Position 1:	_
  Position 2:	_
  Position 3:	_
  Position 4:	G
  Position 5:	_
  Position 6:	_
  Position 7:	_

  
  

• Condition 2: "Only one box is kept between E and G." Since G is at position 4, E can be at position 2 (with box 3 in between) or position 6 (with box 5 in between).
• Condition 3: "U is kept at some place above G." This means U must be in position 1, 2, or 3.
• Condition 4: "T is kept immediately below U." This implies T's position is U's position + 1.
  • If U is at 1, T is at 2.
  • If U is at 2, T is at 3.
  • If U is at 3, T is at 4. This is impossible because G is already at position 4.
  So, the possible pairs for (U, T) are (1, 2) or (2, 3).
• Combining Conditions: Let's revisit the possible positions for E (2 or 6) and the possible pairs for (U, T) {(1, 2), (2, 3)}.
  • If E is at position 2, then U cannot be at 1 (T would be at 2, conflicting with E) or U cannot be at 2 (conflicting with E). This scenario leads to contradictions.
  • Therefore, E must be at position 6.

    Position 1:	_
    Position 2:	_
    Position 3:	_
    Position 4:	G
    Position 5:	_
    Position 6:	E
    Position 7:	_

    
    

• Condition 5: "Only three boxes are kept between E and U." E is at position 6. U must be above G (position 1, 2, or 3).
  • If U is at 1, there are 4 boxes (2, 3, 4, 5) between U and E. Incorrect.
  • If U is at 2, there are 3 boxes (3, 4, 5) between U and E. Correct.
  • If U is at 3, there are 2 boxes (4, 5) between U and E. Incorrect.
  So, U must be at position 2.
• Position of T: Since T is immediately below U (U is at 2), T must be at position 3.

  Position 1:	_
  Position 2:	U
  Position 3:	T
  Position 4:	G
  Position 5:	_
  Position 6:	E
  Position 7:	_

  
  

• Condition 6: "H is not kept immediately above or below E." E is at position 6. H cannot be at position 5 or 7. The available positions are 1, 5, 7. Since H cannot be at 5 or 7, H must be at position 1.

  Position 1:	H
  Position 2:	U
  Position 3:	T
  Position 4:	G
  Position 5:	_
  Position 6:	E
  Position 7:	_

  
  

• Final Placement: The remaining boxes are S and F. The remaining positions are 5 and 7.
  • Condition 7: "S is kept at one of the places above F."
  To satisfy this, S must be placed at position 5, and F must be placed at the lowermost position, 7.

  Position 1:	H
  Position 2:	U
  Position 3:	T
  Position 4:	G
  Position 5:	S
  Position 6:	E
  Position 7:	F

  
  

Conclusion of Arrangement

The final arrangement of the boxes from top (1) to bottom (7) is:

1. H
2. U
3. T
4. G
5. S
6. E
7. F

Therefore, the box kept at the lowermost position (position 7) is F.