The problem states that only one suspect is guilty. The guilty individual lies, while innocent individuals tell the truth.

Let us assume P is the guilty party:

If P is guilty, P's statements must be false.
- P's statement "I did not steal" becomes false, implying P stole the mobile phone.
- P's statement "Q stole it" becomes false, implying Q did not steal the mobile phone.
Now, we examine the statements of Q and R, who must be innocent and therefore truthful:
- Q's statements:
  - "R did not steal" must be true. This is consistent with R being innocent.
  - "I did not steal" must be true. This is consistent with Q being innocent.
- R's statements:
  - "I did not steal" must be true. This is consistent with R being innocent.
  - "I do not know who did it" must be true. This is consistent with R being innocent and unaware of P's guilt.
All statements are consistent under the assumption that P is guilty. Therefore, P stole the mobile phone.

Let us analyze the scenarios where Q or R are assumed guilty:

If Q is guilty:
- Q's statements must be false.
  - Q's statement "I did not steal" becomes false, implying Q stole the mobile phone.
  - Q's statement "R did not steal" becomes false, implying R stole the mobile phone.
- This scenario leads to a contradiction, as both Q and R would be guilty, which violates the problem's condition that only one person is guilty. Therefore, Q cannot be guilty.
If R is guilty:
- R's statements must be false.
  - R's statement "I did not steal" becomes false, implying R stole the mobile phone.
- Now, we examine Q's statements, as Q must be innocent and truthful.
  - Q's statement "R did not steal" must be true.
- This contradicts our initial assumption that R stole the mobile phone. Therefore, R cannot be guilty.
Cannot be concluded:
- As demonstrated, a consistent scenario is established when P is identified as the guilty party, with all statements aligning with the given conditions. Thus, a definitive conclusion can be reached.