Study the following information and answer the related questions: Seven boxes are placed one above the other. They all of are of different weight (only integer value). Total weight of all the boxes is 215kg. No box is less than 24kg and more than 37kg. Only two boxes are placed above box L whose weight is a multiple of 7. Box D is placed four places below box L. The number of boxes placed above D is same as the number of boxes placed below the box whose weight is 3kg less than box L. One box is placed between box L and box F. Weight of box F is a square number. Weight of box B is a prime number which is placed just above box F. Box T is placed above box G but both are not placed adjacent to each other. Weight of box G is equal to the average weight of box B and box F. G’s weight is not an even number. Total weight of box T and box G is 63kg. More than three boxes are placed below box C.

**Question:** How many boxes weigh more than box B?

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Study the following information and answer the related questions: Seven boxes are placed one above the other. They all of are of different weight (only integer value). Total weight of all the boxes is 215kg. No box is less than 24kg and more than 37kg. Only two boxes are placed above box L whose weight is a multiple of 7. Box D is placed four places below box L. The number of boxes placed above D is same as the number of boxes placed below the box whose weight is 3kg less than box L. One box is placed between box L and box F. Weight of box F is a square number. Weight of box B is a prime number which is placed just above box F. Box T is placed above box G but both are not placed adjacent to each other. Weight of box G is equal to the average weight of box B and box F. G’s weight is not an even number. Total weight of box T and box G is 63kg. More than three boxes are placed below box C.

**Question:** How many boxes weigh more than box B?

Accepted Answer

**Solution:**

1. **Identify possible weights for box L:**
   - Box L's weight is a multiple of 7 between 24 and 37.
   - Possible multiples: 28 and 35.

2. **Position of box L:**
   - Two boxes are above L, so L is at position 3 from the top (positions numbered 1 at top to 7 at bottom).

3. **Position of box D:**
   - D is four places below L, so D is at position 7 (3 + 4 = 7).

4. **Number of boxes above D:**
   - D is at position 7, so boxes above D = 6.

5. **Box whose weight is 3 less than L:**
   - If L = 28, then box weight = 25.
   - If L = 35, then box weight = 32.

6. **Number of boxes below the box with weight (L - 3):**
   - This equals the number of boxes above D, which is 6.
   - Since total boxes = 7, if boxes below that box = 6, then that box must be at position 1 (top).

7. **Therefore, the box with weight (L - 3) is at position 1.**

8. **Check L = 35 scenario:**
   - Box with weight 32 at position 1.
   - L at position 3 with weight 35.

9. **One box between L and F:**
   - L is at 3, so F can be at position 1 or 5.
   - Position 1 is taken by box with weight 32.
   - So F is at position 5.

10. **Weight of F is a perfect square between 24 and 37:**
    - Possible squares: 25 and 36.

11. **Box B is prime and just above F:**
    - F is at 5, so B is at 4.
    - Prime numbers between 24 and 37: 29, 31.

12. **Box G's weight is average of B and F, and is odd:**
    - Try F = 25, B = 29: average = (25 + 29)/2 = 27 (odd, valid)
    - Try F = 36, B = 31: average = (36 + 31)/2 = 33.5 (not integer)

So F = 25, B = 29, G = 27.

13. **Positions so far:**
    - 1: Box with weight 32 (L - 3)
    - 3: L = 35
    - 4: B = 29
    - 5: F = 25
    - 7: D
    - G and T remain to be placed at positions 2 and 6.

14. **T is above G but not adjacent:**
    - Possible placements:
      - T at 2, G at 6 (not possible, T not above G)
      - T at 6, G at 2 (T below G, invalid)
      - T at 2, G at 6 (T above G? No, 2 is above 6, so T above G is true)
      - But they are not adjacent (positions 2 and 6 are not adjacent), so T at 2 and G at 6 is valid.

15. **Total weight of T and G is 63:**
    - G = 27, so T = 63 - 27 = 36.

16. **More than three boxes below C:**
    - Positions below C > 3 means C is at position 3 or higher.
    - L is at 3, so C can be at position 1 or 2.
    - Position 1 is taken, so C is at position 2.

17. **Final arrangement:**
    - 1: Box with weight 32 (L - 3)
    - 2: C = 36 (T)
    - 3: L = 35
    - 4: B = 29
    - 5: F = 25
    - 6: G = 27
    - 7: D

18. **Count boxes heavier than B (29):**
    - Boxes heavier than 29: 32, 35, 36
    - That's 3 boxes heavier than B.

19. **Recheck total weight:**
    - Sum = 32 + 36 + 35 + 29 + 25 + 27 + weight of D
    - Sum of known weights = 32 + 36 + 35 + 29 + 25 + 27 = 184
    - Total weight = 215, so D = 215 - 184 = 31

20. **D's weight is 31 (prime, fits the range).**

21. **Now count boxes heavier than B (29):**
    - Boxes heavier than 29: 32, 35, 36, 31
    - Total = 4 boxes.

**Answer:** Four boxes have more weight than box B.

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