From what I can see, winning the queen and thus a winning advantage is the objective of the puzzle, which can be done after 1. Nf8+ K-- 2. Ne6+.
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http://upload.wikimedia.org/wikipedia/commons/c/c6/Sixday.jpg
I saw this image when I was reading about the soviet calendar on wikipedia, when I noticed the chess puzzle, I zoomed in to try to solve it. I found a good solution (exchange a knight for the opponent's queen), but I want to know if I'm missing something, if there is Mate in 2 or 3...
Anyone?