Six boxes – P, Q, R, S, T and U – are stacked one above the other. Each box contains a different item: Pens, Clocks, Bottles, Radios, Cups and Paints. All the information is not necessarily in the same order. The box which contains clocks is placed three boxes below Box T. More than two boxes are placed between Box T and Box Q. The box which is placed two boxes above Box Q contains bottles. The number of boxes above the box which contains bottles is same as the number of boxes placed below Box R. Box P and Box S are placed adjacent to each other. Box S doesn’t contain bottles and pens. Box Q and Box U doesn’t contain Radios. The box which contains radios is placed immediately above the box which contains cups. Box Q doesn’t contain paints. The box which contains paints is not placed below the box which contains Cups.

Which of the following statements is/are incorrect?

I. Box S is placed above Box R.
II. Box R doesn’t contain Clocks.
III. Box T is placed two places below Box P.

To determine which statements are incorrect, let us systematically reconstruct the order and contents of the six stacked boxes from the given clues.

Let the six positions from top to bottom be numbered 6 (top) down to 1 (bottom).

Clue 1: The box containing clocks is placed three boxes below Box T.
This means if Box T is at position $x$, the clock box is at position $x-3$. Thus, Box T can be at position 6, 5, or 4.

Clue 2: More than two boxes are placed between Box T and Box Q.
This implies the number of boxes between T and Q is at least 3. Thus:
- If T is at position 6: Q must be at position 2 or 1.
- If T is at position 5: Q must be at position 1.
- If T is at position 4: Q cannot be placed because we need at least 3 boxes between them.

Clue 3: The box which is placed two boxes above Box Q contains bottles.
If Box Q is at position $y$, the box containing bottles is at position $y+2$. Let's test the possible positions for Q and T:
- Case 1: Q is at 2. Then T is at 6. The box containing bottles is at 4. The clock box is at 3 (three boxes below T, i.e., 6 - 3 = 3).
- Case 2: Q is at 1. Then T can be at 6 or 5. The box containing bottles is at 3.
Let's analyze the number of boxes above bottles:
In Case 1, bottles is at 4. The number of boxes above bottles is 2 (positions 5 and 6).
In Case 2, bottles is at 3. The number of boxes above bottles is 3 (positions 4, 5, and 6).

Clue 4: The number of boxes above the box which contains bottles is same as the number of boxes placed below Box R.
- In Case 1 (bottles at 4, so 2 boxes above it): Box R must have 2 boxes below it, which means Box R is at position 3. But in Case 1, the clocks box is at position 3, which is fine since Box R can contain clocks.
- In Case 2 (bottles at 3, so 3 boxes above it): Box R must have 3 boxes below it, placing Box R at position 4.

Let's look at Case 1 (T at 6, R/Clocks at 3, Bottles at 4, Q at 2):
The remaining positions for boxes are 5 and 1. The boxes left to place are P, S, and U.
Clue 5: Box P and Box S are placed adjacent to each other.
The only available adjacent positions in Case 1 are not there because the empty positions are 5 and 1, which are not adjacent. Thus, Case 1 is invalid.

Let's look at Case 2 where Q is at 1, bottles is at 3, and R is at 4.
Let's test T at 6:
If T is at 6, clocks is at 3 (which is already bottles). This is a contradiction. Thus, T cannot be at 6.
Let's test T at 5:
If T is at 5, clocks is at 2 (5 - 3 = 2). This is valid.
So we have the current arrangement:
Position 6: (Empty)
Position 5: Box T
Position 4: Box R
Position 3: Bottles
Position 2: Clocks
Position 1: Box Q

Now, let's place Box P and Box S.
Clue 5: Box P and Box S are placed adjacent to each other.
The remaining positions for boxes are 6, 3, and 2. The only adjacent positions available among these are 3 and 2. Thus, P and S must occupy positions 3 and 2 in some order.
Consequently, the remaining Box U must be at position 6.
Clue 6: Box S doesn’t contain bottles and pens.
Since Box S cannot contain bottles, S cannot be at position 3 (which contains bottles). Therefore, Box S must be at position 2 (containing clocks), and Box P must be at position 3 (containing bottles).
So the box mapping is:
Position 6: Box U
Position 5: Box T
Position 4: Box R
Position 3: Box P (Bottles)
Position 2: Box S (Clocks)
Position 1: Box Q

Now, let's determine the remaining items (Pens, Radios, Cups, Paints) for U (6), T (5), R (4), and Q (1):
Clue 7: Box Q and Box U do not contain Radios.
So Radios can only be in Box T (5) or Box R (4).
Clue 8: The box containing radios is placed immediately above the box containing cups.
- If Box T (5) contains radios, then Box R (4) must contain cups.
- If Box R (4) contains radios, then Box P (3) must contain cups. But Box P contains bottles. So this is not possible.
Thus, Box T (5) contains Radios, and Box R (4) contains Cups.

We are left with Q (1) and U (6), and items Pens and Paints.
Clue 9: Box Q doesn't contain paints.
Thus, Box U (6) must contain Paints, and Box Q (1) must contain Pens.

Let us check the final complete arrangement:
6. Box U - Paints
5. Box T - Radios
4. Box R - Cups
3. Box P - Bottles
2. Box S - Clocks
1. Box Q - Pens

Now we evaluate the given statements:
I. Box S is placed above Box R.
Box S is at position 2 and Box R is at position 4. So Box S is placed below Box R. This statement is incorrect.
II. Box R doesn’t contain Clocks.
Box R contains Cups. So Box R indeed does not contain Clocks. This statement is correct.
III. Box T is placed two places below Box P.
Box T is at position 5 and Box P is at position 3. Box T is placed two places above Box P. This statement is incorrect.

Since statements I and III are incorrect, the correct option is "Both I and III".