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There is a 3-fold repetition of the position: 9...Ka7 10. Qa4+; 11...Ka7 12. Qa4+; 20...Ka7 21. Qa4+. All pieces on the board are in the same position these three times. However, for White to get a draw under the 3-fold repetition rule, he must CLAIM the draw, and he must have time remaining on his clock when he claims the draw. I don't understand from your presentation of this problem whether your opponent actually claimed a draw with time still on his clock after his final move 21. Qa4+ gave him the 3-fold repetition position.
Nalimov Tablebase says this is a win for Black, but that's beside the point really. Your opponent has to do more than show that a threefold repetition can be forced. He actually has to create the threefold repetition.
Its a win because the king isn't in the drawing zone for a knight pawn in a queen and queen+ pawn endgame
If you're behind on the board, and on the clock in a final time control, whether it's blitz, bullet or standard chess, don't complain about your opponent striving to win.
If it's a draw, prove it.
This very simple guys, my opponent lost on time, after I claimed the flag he insist that it's a draw, I keep score, my score is a win on time, my opponent doesn't like to lose, he put on his score keeping pad it is a draw, come people I claimed the win on time after 3 seconds ran out, period. The point is don't claim anymore post mortem anaylsis as if the game is still on chess rule is when one of the flag fell or time out the one with zero time has lost the game!
10. 12. and 21. are all the same. it's a draw.
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