My partner Doug tipped me to this video about sudoku with a couple of chess rules added. I actually know how this concept works, even though I can't do it myself. The extra rules create a distinct pattern within the numerical possibilities, which is visible from the perspective of high enough logical-mathematical intelligence, so once you start poking at it, they pop right up. If you want to know what it's like to be a genius at this level, listen to the guy explain how the puzzle leads you through its solution. :D
It's pretty much the same as what happens in form poetry, only with numbers instead of words.