Six boxes A, B, C, D, E and F have been painted with six different colours viz. violet, indigo, blue, green, yellow and orange and arranged from left to right (not necessarily either kept or painted with the colours in the same order). Each box contains a ball of any one of the following six games: cricket, hockey, tennis, golf, football and volleyball (not necessarily in the same order). The golf ball is in violet box and is not in the box D. The box A which contains tennis ball is orange in colour and is at the extreme right. The hockey ball is neither in box D nor in box E. The box C having cricket ball is painted green. The hockey ball is neither in the box painted blue nor in the box painted yellow. The box C is fifth from right and next to box B. The box B contains volleyball. The box containing the hockey ball is between the boxes containing golf ball and volleyball.

Which of the following statements is/are correct ?

The correct option is: F is painted indigo.

Let us analyze the puzzle step-by-step to determine the color, game, and position of each box.

Step 1: Understand the constraints and identify positions.
There are 6 boxes: A, B, C, D, E, and F.
Let us represent their positions from left to right as: 1, 2, 3, 4, 5, 6.
- "The box A is at the extreme right." This means Box A is at position 6.
- "The box C is fifth from right." Counting from the right (6 is 1st, 5 is 2nd, 4 is 3rd, 3 is 4th, 2 is 5th), Box C is at position 2.
- "The box C is next to box B." Since C is at position 2, B can be at position 1 or 3.
- "The box containing the hockey ball is between the boxes containing golf ball and volleyball."
- "Box B contains volleyball."
- "The golf ball is in the violet box."
Since the box with the hockey ball is between golf (violet) and volleyball (Box B), the volleyball box (B) and golf box (violet) must be separated by exactly one box, which contains the hockey ball. Thus, the order of these three boxes must be B (volleyball) - Hockey - Golf (violet), or Golf (violet) - Hockey - B (volleyball).

Step 2: Placing Box B, Hockey, and Golf (Violet).
- If B is at position 1: then the hockey box must be at position 2, and the golf box at position 3. But we know Box C is at position 2 and contains the cricket ball. This is a contradiction.
- Therefore, B must be at position 3. Since B (volleyball) is at position 3, the hockey box must be at position 4, and the golf (violet) box must be at position 5. (It cannot be B at 3, hockey at 2, golf at 1, because C is at position 2 with cricket).
So, we have:
Position 1: [Unknown Box]
Position 2: Box C (Cricket, Green)
Position 3: Box B (Volleyball)
Position 4: [Unknown Box] (Hockey)
Position 5: [Unknown Box] (Golf, Violet)
Position 6: Box A (Tennis, Orange)

Step 3: Determining the remaining boxes and colors.
- We are told "The golf ball... is not in the box D." Since the golf ball is at position 5, Box D cannot be at position 5.
- "The hockey ball is neither in box D nor in box E." Since hockey is at position 4, Box D and Box E cannot be at position 4. Thus, the box at position 4 must be Box F.
- Since Box D cannot be at 4 or 5, Box D must be at position 1.
- Since Box E cannot be at 4, Box E must be at position 5 (containing the golf ball).
Now we have the box assignments for all positions:
Position 1: Box D
Position 2: Box C (Cricket, Green)
Position 3: Box B (Volleyball)
Position 4: Box F (Hockey)
Position 5: Box E (Golf, Violet)
Position 6: Box A (Tennis, Orange)

Step 4: Finding the colors of the remaining boxes (D, B, F).
The remaining colors are: indigo, blue, yellow.
- "The hockey ball (Box F) is neither in the box painted blue nor in the box painted yellow." Therefore, Box F must be painted indigo.
This directly confirms the statement "F is painted indigo" is correct.