Three 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:

No chess is a can.

Not a single can is a horn.

Every horn is an adapter.

Conclusions:
I. Some adapters which are horns are chess as well.
II. No chess is a horn.
III. Some adapters are horns.

Let's analyze the statements using Venn diagrams:
"No chess is a can" → Chess and Can have no intersection.

"Not a single can is a horn" → Can and Horn have no intersection.

"Every horn is an adapter" → All Horns are inside Adapters.

Now let's evaluate the conclusions:

Conclusion I: "Some adapters which are horns are chess as well." → This means there is a mandatory intersection between Horn and Chess. Since there is no definite relation given between Chess and Horn, this is not definitely true.

Conclusion II: "No chess is a horn." → While they can be separate, there is no direct negative statement between Chess and Horn. They could potentially overlap. Thus, it does not follow definitely.

Conclusion III: "Some adapters are horns." → Since "Every horn is an adapter", the part of adapters containing horns will always be horns. Hence, this conclusion definitely follows.

Therefore, only conclusion III follows.