Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some prizes are papers.
All papers are certificates.

Conclusions:
I. Some certificates are papers.
II. Some certificates are prizes.
III. Some papers are prizes.

Let's map out the conditions:
Some prizes are papers: There is an intersection between the 'prizes' circle and the 'papers' circle.

All papers are certificates: The entire 'papers' circle is contained within the 'certificates' circle.

Let's evaluate the conclusions:

Conclusion I: Some certificates are papers. Since all papers are certificates, the portion of certificates containing papers ensures that some certificates are indeed papers. This follows.

Conclusion II: Some certificates are prizes. Since some prizes are papers, and all papers are inside certificates, the intersecting region of prizes and papers must also be inside certificates. Thus, some certificates are prizes. This follows.

Conclusion III: Some papers are prizes. Since 'Some prizes are papers' is true, its converse 'Some papers are prizes' is automatically true. This follows.

Therefore, all conclusions follow.