Which among the following statement(s) is/are true?
I. No box is kept below box F
II. Box D is kept below box C
III. Box A is not red in colour

Study the following information carefully and answer the questions given below:
Six paint boxes are kept one above another in the form of the stack. Each box has different colours paint- Pink, Blue, Red, White, Yellow and Grey but not in same order as given.
Yellow coloured box is kept three boxes above box B. Box D is kept adjacent to box B. As many boxes are kept above box D as below red coloured box. Box E is kept immediately below red coloured box. Box B is not red in colour. More than one box is kept between box E and the grey coloured box. Box D is kept above grey coloured box. Box A is kept above the white coloured box but below box C. Box B is not kept below white coloured box. More than one box is kept between box F and blue coloured box. Pink coloured box doesn’t keep adjacent to blue coloured box.

The correct answer is Both I and II.

Let us solve the puzzle step-by-step to determine the order of the six paint boxes from top to bottom (Positions 6 to 1, where 6 is the topmost position and 1 is the bottommost position), along with their respective colors.

Step 1: Understand the given clues

1. Six paint boxes are kept one above another (Positions 6, 5, 4, 3, 2, 1).

2. The colors of the boxes are Pink, Blue, Red, White, Yellow, and Grey.

3. Yellow coloured box is kept three boxes above box B. This means there are 2 boxes between the Yellow box and Box B (Yellow _ _ B).

4. Box D is kept adjacent to box B.

5. As many boxes are kept above box D as below red coloured box.

6. Box E is kept immediately below red coloured box.

7. Box B is not red in colour.

8. More than one box is kept between box E and the grey coloured box.

9. Box D is kept above grey coloured box.

10. Box A is kept above the white coloured box but below box C (Order: C ... A ... White).

11. Box B is not kept below white coloured box, meaning Box B is kept above the White box.

12. More than one box is kept between box F and blue coloured box.

13. Pink coloured box doesn't keep adjacent to blue coloured box.

Step 2: Placing the boxes step-by-step

From Clue 10 and 11: Box C is above Box A, Box A is above White, and Box B is above White. Therefore, White must be at a lower position.

Consider the placement of Yellow and Box B (Yellow _ _ B):

If Yellow is at Position 6, Box B is at Position 3.

If Yellow is at Position 5, Box B is at Position 2.

Let's evaluate Box B at Position 3 (Yellow at Position 6):

- Box D is adjacent to B, so Box D can be at Position 4 or Position 2.

- If Box D is at Position 4: Boxes above D = 2 (Positions 5 and 6). So, boxes below Red box = 2, which puts Red box at Position 3. But B is at Position 3 and B is NOT Red (Clue 7). Thus, D cannot be at Position 4.

- If Box D is at Position 2: Boxes above D = 4 (Positions 3, 4, 5, 6). So, boxes below Red box = 4, which puts Red box at Position 5. Box E is immediately below Red box, so Box E is at Position 4.

Let's check the remaining arrangements for Box B at Position 3, Yellow at Position 6, D at Position 2, Red at Position 5, E at Position 4:

- Clue 8: More than 1 box between Box E (Position 4) and Grey box. Grey can only be at Position 1 (2 boxes in between: 2 and 3). This satisfies Clue 9 (Box D at 2 is above Grey at 1).

- Clue 10 & 11: Box B is at 3, Box D at 2, Grey at 1. Since Box B is above White, and Box A is above White, White must be at Position 2 or 1. Grey is at 1, so White box must be at Position 2 (Box D is White).

- Now we need positions for Box C, Box A, and Box F: Available positions for boxes are 6, 5, and 1.

- Clue 10 states: Box A is kept above White (Position 2) but below Box C. So C must be at Position 6, and A must be at Position 5. This leaves Box F for Position 1.

Step 3: Verification of Box Positions and Colors

Positions from Top (6) to Bottom (1):

Position 6: Box C - Yellow

Position 5: Box A - Red

Position 4: Box E - (Pink or Blue)

Position 3: Box B - (Pink or Blue)

Position 2: Box D - White

Position 1: Box F - Grey

Color allocations:

- Position 5 (Box A) is Red.

- Position 6 (Box C) is Yellow.

- Position 2 (Box D) is White.

- Position 1 (Box F) is Grey.

- Position 4 (Box E) and Position 3 (Box B) are Pink and Blue.

- Clue 12: More than 1 box between Box F (Position 1) and Blue coloured box. If Blue is at Position 3, there is only 1 box between them (Position 2), which violates "more than one box". Therefore, Blue must be at Position 4 (Box E), leaving Pink at Position 3 (Box B).

Final complete stack from top to bottom:

6. Box C - Yellow

5. Box A - Red

4. Box E - Blue

3. Box B - Pink

2. Box D - White

1. Box F - Grey

Step 4: Evaluate the Given Statements

I. No box is kept below box F: True, since Box F is at the bottom (Position 1).

II. Box D is kept below box C: True, since Box D is at Position 2 and Box C is at Position 6.

III. Box A is not red in colour: False, because Box A is Red in colour.

Therefore, statements I and II are true.