When puzzles combine varying types of clues together it is easy for one to dominate, leaving the puzzler feeling like the added complexity was simply a waste. Sometimes two different clues come together nicely, and both feel like they're pulling the work of making the puzzle fun. That's what I feel happened here.
For our purposes, let the range of a set of four numbers be the smallest interval containing all of them. Thus, if our numbers are 4, 9, 6, 3 then our range would be [3,9]. In this puzzle, clues between four cells give the range of the numbers in those cells, but only when those four numbers are imbalanced in the sense that they have three odds and one even or three evens and one odd. A clue of 'B' between four entries indicates there are the same number of evens as odds, but tells us nothing about the range. Finally, some clues are left out to increase the difficulty.
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