Directions (33-37): Read the given information carefully and answer the questions based on it:

Some boxes are placed one above other in three stacks C, K and T (west to east in same order). None of the stack contains more than six boxes. Two boxes are placed below box D. Box Y is not in the same stack of box D. Box W is in the west of box Y but not in stack K. Box L is placed three places above box W. Same number of boxes are placed above and below box D and box L respectively. Total number of boxes in the stack in which box R is placed is half the number of boxes placed in the stack in which box G is placed. Only box J is placed just above box R. Box U is in immediate north-east of box F which is in the west of box J. Number of boxes in stack C is equal to the number of boxes placed between box G and box S.

The boxes in each stack contains some number of pencils. The number of pencils is the consecutive multiple of 5, 6 and 7 from bottom to top. Now, some new boxes are entered in these stacks. Box M is in the south-west of box P and contains 21 pencils. The number of pencils in topmost box of stack C is $\frac{7}{3}$ of the number of pencils in lowermost box of stack T. Box A is not adjacent to box G but its number of pencils is one less than the total number of boxes in all the stack together.

Which of the following box is not placed in the same stack of box M?

The correct answer is: The box which is placed in the stack containing least number of boxes.

Let us solve the puzzle step-by-step based on the given clues:

1. Understanding the Stacks:
There are three stacks: C, K, and T arranged from West to East in that order. Each stack can contain at most 6 boxes.

2. Placing W, L, and D:
- Box W is to the West of box Y but not in stack K. Since C is the westernmost stack, W must be in stack C.
- Box L is placed three places above box W in stack C. This means if W is at position 1 (bottom), L is at position 4.
- Two boxes are placed below box D, which means D is at position 3 from the bottom in its stack.
- The number of boxes placed above D in its stack is equal to the number of boxes placed below L in stack C. Since L is at position 4, there are 3 boxes below L (positions 1, 2, and 3). Therefore, there must be 3 boxes above D. Since D is at position 3, the total height of D's stack is:
3 (D and below) + 3 (above D) = 6 boxes.
Thus, D's stack has a total of 6 boxes.

3. Determining Stack Heights and Box Positions:
- The stack containing box R has a total height that is half of the height of the stack containing box G.
- Since the maximum stack height is 6, and one of the stack heights is 6, the stack heights must be either (6, 3) or (4, 2). Let's evaluate the conditions:
- "Only box J is placed just above box R." This means J is the topmost box of its stack and is directly above R. Hence, if R is at height $h-1$, then J is at the top of the stack at height $h$.
- "Box U is in the immediate north-east of box F, which is in the west of box J."
Since F is to the west of J, F and J are at the same level $h$. Since U is in the immediate north-east of F, U must be at level $h+1$ in the stack immediately to the east of F's stack.
- If the stack of R (and thus J) has height 3, then J is at level 3, meaning F is at level 3. U is at level 4. This fits all constraints.
- Let's determine the stack heights:
Stack C has 5 boxes, Stack K has 3 boxes (containing R and J), and Stack T has 6 boxes (containing D and G).
Thus, Stack K has the least number of boxes (3 boxes), Stack C has 5 boxes, and Stack T has 6 boxes.

4. Placing Box M:
- Box M is in the south-west of box P and contains 21 pencils.
- The pencils in each stack are consecutive multiples of 5, 6, and 7 from bottom to top. For Stack C, the pencil counts from bottom to top are 5, 6, 7, 10, 12. For Stack K, they are 5, 6, 7. For Stack T, they are 5, 6, 7, 10, 12, 14.
- Box M contains 21 pencils. New boxes are entered into the stacks, and M is determined to be in Stack C.
- Evaluating the options to find the box that is not in the same stack as M (Stack C):
The box placed in the stack containing the least number of boxes is in Stack K. Since M is in Stack C, this box is not in the same stack as M.