Question

In a football tournament, Kim, Jim, and Tim are the top three scorers in any order. When asked about the ranking, each of them said two sentences, one of which is true, and the other is false.
Kim: I got the top score; Jim was third.
Jim: I got the top score; Kim was second.
Tim: I got the top score; Jim was second.

Considering all the three statements together, find out who the second scorer was.

Answer 1

Case 1:
Let's assume Kim is the top scorer.
Kim: I got the top score. Jim was third.
Only one of his statements is true.
We consider his 1st statement to be true.
Hence, the second statement is false.
Jim is not third, and it means that Jim is second and Tim is third.
Let's verify this with the other statements.
Jim: I got the top score; Kim was second.
Tim: I got the top score; Jim was second.
For both of them, the 1st statement is false; hence, the second one must be true.
But their second statements are contradictory. Hence, this case is rejected.

Case 2:
Let's assume Jim is the top scorer.
Jim: I got the top score; Kim was second.
Only one of his statements is true.
We consider his 1st statement to be true.
Hence, the second statement is false.
Kim is not second; it means that Kim is third and Tim is second.
Let's verify this with the other statements.
Kim: I got the top score; Jim was third.
Tim: I got the top score; Jim was second.
For both of them, 1st statement is false; hence, the second one must be true.
But their second statements are contradictory. Hence, this case is rejected.

Case 3:
Let's assume that Tim is the top scorer.
Tim: I got the top score; Jim was second.
Only one of his statements is true.
We consider his 1st statement to be true.
Hence, the second statement is false.
Jim is not second, and it means that Jim is third and Kim is second.
Let's verify this with the other statements.
Kim: I got the top score; Jim was third.
Jim: I got the top score; Kim was second.
For both of them, 1st statement is false; hence, the second one must be true.
Their statements are valid.

Hence, the correct order is
1st: Tim
2nd: Kim
3rd: Jim

So, Kim is the second scorer.