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Trying to figure out how to raise you puzzle score whether or not you understand why? Just want those beautiful green checkmarks? I find that at least with puzzles at least going up until the rating of 1200, the solution 80% of the time is simply whatever puts the other side in check. For multi-step puzzle, this is also more often than not true for the remaining steps, or until there is an obvious free material capture opportunity that emerges. Repeat until solved, higher scored and none the wiser.
Conversely, this explains why the I never seemed to be able to apply lessons from the puzzles to my actual games, since I almost never get that double rook battery so many puzzles use to begin with... Simply putting the other side in check whenever possible is *NOT* an effective strategy in actual games. Just in the puzzles.