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.

The football is in the box of which colour?

The correct option is Cannot be determined as data are inadequate.

To understand why this is the correct answer, let us systematically analyze the given statements and arrange the boxes, their colors, positions, and contents step-by-step from left to right (positions 1 to 6).

Let the 6 positions from left to right be:
1 (extreme left), 2, 3, 4, 5, 6 (extreme right).

Step 1: Determine the positions of the boxes.
- "The box A which contains tennis ball is orange in colour and is at the extreme right."
Therefore, Position 6 = Box A (Orange, Tennis).
- "The box C is fifth from right and next to box B."
Counting fifth from the right:
6 is 1st from right,
5 is 2nd from right,
4 is 3rd from right,
3 is 4th from right,
2 is 5th from right.
So, Position 2 = Box C. Since C is green and has the cricket ball ("The box C having cricket ball is painted green"), we have:
Position 2 = Box C (Green, Cricket).
- Since C (Position 2) is "next to box B", Box B must be at either Position 1 or Position 3.
- "The box B contains volleyball." So Box B (Volleyball) is either at Position 1 or Position 3.

Step 2: Locate the Hockey ball.
- "The box containing the hockey ball is between the boxes containing golf ball and volleyball."
This means the boxes for Golf, Hockey, and Volleyball are adjacent in some order (either Golf - Hockey - Volleyball, or Volleyball - Hockey - Golf).
- "The golf ball is in violet box..."
- Since Cricket is at Position 2 and Tennis is at Position 6, the remaining items (Golf, Hockey, Volleyball) must occupy contiguous positions because Hockey is directly between Golf and Volleyball.
- This group of three (Golf, Hockey, Volleyball) can only fit in either positions 3, 4, 5 or positions 1, 2, 3. But Position 2 is already occupied by Cricket. Thus, the three boxes must occupy Positions 3, 4, and 5.
- Since Volleyball is in Box B, Box B must be at Position 3 (next to Box C at Position 2). Therefore:
Position 3 = Box B (Volleyball).
Position 4 = Hockey ball box.
Position 5 = Golf ball box (Violet color).
- From this, we also deduce the remaining position for the last sport, Football, which must be at Position 1.
Position 1 = Football ball box.

Step 3: Analyze the properties of the remaining boxes.
Let us summarize the positions, contents, and colors we have determined so far:
- Position 1: Box ? (Color: ?, Sport: Football)
- Position 2: Box C (Color: Green, Sport: Cricket)
- Position 3: Box B (Color: ?, Sport: Volleyball)
- Position 4: Box ? (Color: ?, Sport: Hockey)
- Position 5: Box ? (Color: Violet, Sport: Golf)
- Position 6: Box A (Color: Orange, Sport: Tennis)

Now let's identify the box labels for the remaining positions (1, 4, and 5):
- The remaining boxes to place are D, E, and F.
- "The golf ball is in violet box and is not in the box D." Since Golf is at Position 5, Position 5 is not Box D.
- "The hockey ball is neither in box D nor in box E." Since Hockey is at Position 4, Position 4 is not Box D and not Box E. Thus, Position 4 must be Box F.
- Since Position 4 is Box F, Box D must be at Position 1 (since it cannot be at Position 5 either).
- Consequently, Box E must be at Position 5.
Let us check this with the clue: "The hockey ball is neither in box D nor in box E." This is satisfied since Hockey is in Box F.

So, the updated distribution is:
- Position 1: Box D (Color: ?, Sport: Football)
- Position 2: Box C (Color: Green, Sport: Cricket)
- Position 3: Box B (Color: ?, Sport: Volleyball)
- Position 4: Box F (Color: ?, Sport: Hockey)
- Position 5: Box E (Color: Violet, Sport: Golf)
- Position 6: Box A (Color: Orange, Sport: Tennis)

Step 4: Determine the colors.
- The remaining colors to place are Indigo, Blue, and Yellow (placed at Positions 1, 3, and 4).
- "The hockey ball is neither in the box painted blue nor in the box painted yellow."
Since Hockey is at Position 4, Position 4 cannot be Blue or Yellow. Therefore, Position 4 (Box F) must be painted Indigo.
- This leaves the colors Blue and Yellow for Position 1 (Box D) and Position 3 (Box B).
- There are no further clues to differentiate between the colors of Box D (Position 1) and Box B (Position 3). Thus, either Box D is Blue and Box B is Yellow, or Box D is Yellow and Box B is Blue.

Conclusion:
Since the football is in Box D (Position 1), its color could be either Yellow or Blue. Because the given information is insufficient to determine which of these two colors belongs to Box D, the color of the box containing the football cannot be determined. Thus, the correct answer is indeed "Cannot be determined as data are inadequate".