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Has anyone got an answer for 7? I think I have the rest of them, (whether I'm correct or not obviously remains to be seen).
#7 is somewhat famous, and there are plenty of articles available on it if you google for the name of it.
Ahhhh... seems really obvious in retrospect. Thanks.
Think about what happens when you lay down any domino on that chessboard.
My dad had two of Gardner's books. I loved puzzling over them as a kid - enough that I bought my own copies for my kids to discover. I credit those books with much of my interest in logic.

Gardner's puzzles always had a beautiful simplicity to them. The solutions are sometimes fiendishly hard, but the problem is always accessible to the layman - no great grasp of mathematics is needed, just the ability to think logically and rigorously.

http://www.amazon.com/Mathematical-Logic-Puzzles-Dover-Recre...

http://www.amazon.com/Entertaining-Mathematical-Puzzles-Mart...