Strange situation. Can King beat the Queen?
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No, not possible
Chess is a turn based game. Black king would be in check first.
1. ...Ke8 2. Ke2 and White should win easilg regardless of what Black plays next.
2. ...Ra8 and 2. ...Rb8 is met by 3. Qg8+ and the rook is gone.
2. ...Rc8 3. Qg8+ Kd7 4. Qg4+ Kc7 (4. ...Kd8 5. Bb6+ and the rook dies.) 5. Bb6+ Kb7 (5. ...Kb8 6. Qd7 and mate can only be avoided with the cost of the rook 6. ...Re8+ 7. Qxe8+.) (5. ...Kxb6 6. Qxc8.) 6. Qd7+ Kb8 (6. ...Kxb6 7. Qxc8.) (6. ...Ka8 7. Qxc8#.) 7. Ba7+ Ka8 8. Qxc8+ and the rook is lost.
2. ...Rd7 3. Qg8+ Ke7 4. Bc5+ Ke6 5. Qg4+ and the rook bids goodbye.
2. ...Rd6 3. Qg8+ Kd7 (3. ...Ke7 4. Bc5 wins the rook.) and the continuation should be longer, but White should also win with material advantage.)
2. ...Rd5 3. Qg8+ and 4. Qxd5.
2. ...Rxd4 3. Qxd4.
If you were playing a chess variant called war, then you could take the queen
Short answer: no.
White cant move the bishop, so can black King beat the Queen?