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THE PLAY-OFF for the 2048 championship of the Dunmatin Home for Bewildered Grandmasters was a tense struggle. Once again, old Garry and even older Anatoly had tied for first place and the whole building felt the tension as they Zimmered their way to the board for the four-game quick-play decider.

In fact, it wasn't all that quick. Under the new rules of the Bobby Fischer clock Mark II, which had been launched on Fischer's 80th birthday, each player received an extra minute per move for each year of his life. So the games dragged on a bit. After days of tense struggle, there was a huge commotion at the board when they had reached this position.

Old Anatoly, playing White, who had just made his move, suddenly tried to retract it. The arbiter rushed in to stop him as Anatoly moaned: "But I could have mated him. In one move. I missed a mate in one." The arbiter, furious at this breach of protocol, declared the game a draw.

Then in the second game, they reached the position at the top of the next column and the same thing happened again. Only this time it was Old Garry who tried to take his move back, protesting that he had missed a mate in one. The third game reached this position:

and the fourth this one:

All you have to do is work out in each case what White had just played, and what mate he missed.

Answers: A: c2-c4 had been played; d5 is mate. B: b4xc5 was played; d5xc6 e.p. was mate. C: b5xc6 e.p was played; d7 is mate. D: c6-c7 played; d8=N is mate.

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