Who is the jester?

The knight cannot say "I am a knave", as that is a false statement.

Similarly, the knave cannot say "I am a knave", as that is a true statement.

Thus, the only person that can say "I am a knave" would be the jester. Hence Bogdan is the jester.

Note: We do not know who the knight or knave actually is. Both of them can legitimately say "I am not a knave".

Only a jester can lie and say: “I am a knave.”

he knave would never claim to be the knave and the knight would never claim to be the knave, it must be Bogdan.

Here, A, B, C are the people (first letter of each name). 1) knight never tells that he is a knave But B told that he is a knave, so, B can't be knight! so, B= jester or knave 2) Let us suppose if A is knight, then, A=knight B=knave or jester C=knave or jester 3) =>If B is jester then C is knave is possible But=> if B is knave and C is jester then B always tells lies so, he can't tell the truth that he is knave, but he tells so.-> so this assumption is wrong. so, A=knight B=jester C=knave 4) Let us suppose if C is knight, then A=knave or jester B=knave or jester C=knight Point 3 applies even here, then, A=knave B=jester C=knight ============>To conclude in any case, B becomes the jester