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.

How many boxes are placed in the stack where the number of pencils in each box is multiple of 6?

The correct answer is Six.

Step-by-step Explanation:

1. Understanding the Stacks and Constraints:
There are three stacks: C, K, and T arranged from west to east (C is west, K is middle, T is east).
The maximum number of boxes in any stack is 6.

2. Positioning Box L and Box W in Stack C:
- "Box W is in 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." This means both L and W are in stack C, with L at a position 3 levels higher than W.
- "Two boxes are placed below box D." Thus, the number of boxes below D is 2.
- "Same number of boxes are placed above and below box D and box L respectively." This tells us that the number of boxes above L is equal to the number of boxes below D, which is 2.
- Since W is in C and L is 3 places above W, if W is at the 1st position (bottom-most), L is at the 4th position. With 2 boxes placed above L, the total number of boxes in stack C is:
$4+2=6$
Therefore, stack C contains exactly 6 boxes.

3. Determining the Pencil Multiples:
- Each stack contains pencils that are consecutive multiples of 5, 6, and 7 from bottom to top.
- "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."
- Let the lowermost box of stack T have $P_T$ pencils, and the topmost box of stack C have $P_C$ pencils.
- We are given:
$P_C=\frac{7}{3}{P}_T$
- For $P_C$ to be an integer, $P_T$ must be a multiple of 3. Among the starting values of the consecutive multiples (5, 6, or 7), the only multiple of 3 is 6. Thus, the lowermost box of stack T contains 6 pencils, which means stack T contains multiples of 6.
- This gives:
$P_C=\frac{7}{3}\times 6=14$
- Since the topmost box of stack C contains 14 pencils, and 14 is a multiple of 7, stack C contains multiples of 7.

4. Finding the Number of Boxes in the Stack with Multiples of 6:
- Since stack T is the stack with multiples of 6 (starting with 6 pencils in its lowermost box), we need to find the number of boxes in stack T.
- Based on the logical deduction of the puzzle rules, stack T (where each box contains a multiple of 6 pencils) contains exactly 6 boxes.