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Those three statements are all true. The cannon must jump over exactly one piece (of either color) in order to capture.
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In the picture above the black cannon at f12 is putting the white king in check. Is that correct for a standard cannon movement? If no, I have to fix some code. I went to piece-o-pedia and the cannon must jump a screen for the attack. Am I correct with the following statements:
1) the white king is not in check
2) the black cannon at f12 can not attack anything due to a mess of black pieces in front of it.
3) the white cannon at g1 can take cannon g12
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I think I am correct, but I want to check with my fellow chess players to confirm that I understand the cannon capture move.