## Task 1 - 310721

Matthias, Thomas, Frank, and Sven were playing football in the courtyard of the apartment buildings. A window pane broke; exactly one of the four boys broke it with a failed goal attempt. They now make the following statements:

Matthias: It was Thomas or Frank who broke the pane.

Thomas: I didn't do it.

Frank: Neither did I.

Sven: Frank did it.

Rolf, who observed everything, notes that at least three of these four statements are true. Investigate whether, if Rolf's observation is true, it can be determined unambiguously who broke the pane! If this is the case, identify the culprit!
In the following table, for each of the four suspects, it is indicated which of the four statements are true (t) and which are false (f):

| Suspect | Matthias | Thomas | Frank | Sven |
| :--- | :---: | :---: | :---: | :---: |
| Matthias | $\mathrm{f}$ | $\mathrm{t}$ | $\mathrm{t}$ | $\mathrm{f}$ |
| Thomas | $\mathrm{t}$ | $\mathrm{f}$ | $\mathrm{t}$ | $\mathrm{f}$ |
| Frank | $\mathrm{t}$ | $\mathrm{t}$ | $\mathrm{f}$ | $\mathrm{t}$ |
| Sven | $\mathrm{f}$ | $\mathrm{t}$ | $\mathrm{t}$ | $\mathrm{f}$ |

Only if Frank was the culprit, at least three of the statements are true. Therefore, this condition uniquely determines that only Frank could have broken the window.