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?

To solve this puzzle, we need to determine the positions of the boxes, the games they contain, and their colors. We'll arrange them from left to right (positions 1 to 6).

1. "The box A which contains tennis ball is orange in colour and is at the extreme right." Position 6: A (Tennis, Orange)

2. "The box C is fifth from right". In a 6-position arrangement (1-2-3-4-5-6), the 5th from the right is position 2. Position 2: C

3. "The box C having cricket ball is painted green." Position 2: C (Cricket, Green)

4. "The box C is ... next to box B." So B is at position 1 or 3. "The box B contains volleyball."

5. "The box containing the hockey ball is between the boxes containing golf ball and volleyball." This means the hockey box is numerically between the golf and volleyball boxes, but not necessarily immediately adjacent.

   • If B is at Position 1 (Volleyball), then Hockey (H) would be at P2 or P3, and Golf (G) further right. If H is at P2, it conflicts with C (Cricket).
   • If B is at Position 3 (Volleyball), then the sequence could be G-H-V, where G is at P1, H at P2, and V at P3. However, P2 is C (Cricket), which conflicts with Hockey.
   • Let's reconsider "between" not meaning immediate adjacency. If B (Volleyball) is at P3. For Hockey to be between Golf and Volleyball, and not conflict with C at P2, Hockey must be at P4 and Golf at P5. (G-H-V sequence: P5-P4-P3). This is consistent.

Let's finalize the game positions based on B at P3, and G-H-V as P5-P4-P3: Position 1: ? Position 2: C (Cricket, Green) Position 3: B (Volleyball) Position 4: Hockey Position 5: Golf Position 6: A (Tennis, Orange)

6. The remaining game is Football, which must be at Position 1. Position 1: Football

Now, let's place the remaining boxes (D, E, F) and colors (violet, indigo, blue, yellow).

7. "The golf ball is in violet box and is not in the box D." Golf is at P5. So P5 is (Golf, Violet). The box at P5 is not D.

8. "The hockey ball is neither in box D nor in box E." Hockey is at P4. So the box at P4 is not D and not E. This means the box at P4 must be F. Position 4: F (Hockey)

9. From step 7, the box at P5 (Golf, Violet) is not D. The remaining boxes for P1 and P5 are D and E. So, the box at P5 must be E. Position 5: E (Golf, Violet)

10. The remaining box is D, which must be at P1. Position 1: D (Football)

So the complete arrangement of Boxes and Games is: Position: 1 (D, Football) | 2 (C, Cricket) | 3 (B, Volleyball) | 4 (F, Hockey) | 5 (E, Golf) | 6 (A, Tennis)

Now for the colors: Position: 1 (D, Football, ?) | 2 (C, Cricket, Green) | 3 (B, Volleyball, ?) | 4 (F, Hockey, ?) | 5 (E, Golf, Violet) | 6 (A, Tennis, Orange)

11. "The hockey ball is neither in the box painted blue nor in the box painted yellow." Hockey is in F (at P4). F's color is not Blue and not Yellow. The remaining colors are Indigo, Blue, Yellow. So F must be Indigo. Position 4: F (Hockey, Indigo)

12. The remaining colors are Blue and Yellow, for boxes D (at P1) and B (at P3). We don't have enough information to definitively assign Blue or Yellow to D or B.

Let's evaluate the given statements:

A) D is painted yellow D is at Position 1. Its color could be Yellow or Blue. This statement cannot be confirmed.

B) F is painted indigo F is at Position 4. Its color is Indigo. This statement is CORRECT.

C) B is painted blue B is at Position 3. Its color could be Blue or Yellow. This statement cannot be confirmed.

D) All of the above Incorrect, as A and C are not confirmed.

The final answer is B.

The final arrangement: Position: 1 2 3 4 5 6 Box: D C B F E A Game: Football Cricket Volleyball Hockey Golf Tennis Color: Yellow/ Green Blue/ Indigo Violet Orange Blue Yellow

The final answer is B