I just finished reading Alice in Puzzle-Land by Raymond Smullyan, and was inspired to come up with a couple logic puzzles of my own.
When she was a girl, the White Queen practiced believing impossible things for half an hour every day. Once, when she was practicing, she overheard two bishops having the following conversation:
B1: At least one of us is red.
B2: I never step on squares of my own colour.
B1: I never step on red squares.
B2: We are both the same colour.
The White Queen believed everything they said. Assuming the court contains only those pieces normally found in a single chess set, and follows the normal rules of chess, how many impossible things did she believe?
The next day, the White Queen overheard another conversation between two knights:
K1: Knights always tell the truth.
K2: Bishops always lie.
The White Queen believed these statements, but no longer necessarily believed what the bishops said on the previous day. Did she believe any impossible things?