I'm trying to get better by doing many tactics puzzles a day. This one I found very interesting.
[FEN "6rk/6rp/p3pQ2/3pP3/3Pb3/1PP1PRR1/4q2P/6K1 w - - 0 1"] 1. Qxg7+! Rxg7 2. Rf8+ Rg8 3. Rxg8#
I'm trying to figure out what should have jumped out at me in order for me to have seen it. Of course, my typical heuristic sequence involves finding forcing moves (which is how I solved it in the first place), but that doesn't help me learn from the structure of the position. I'm trying to figure out what the intuition behind the position is. Here's an example of what I mean by intuition; take this puzzle for instance.
[FEN "8/8/8/q4k2/8/8/8/4K2R w - - 0 1"] 1. Rh5+ Kg6 2. Rxa5
In this puzzle, the intuition is that the queen is in the same line of sight (from a rook's perspective) as the king, and so if the king is checked along that line of sight, he must move off of it, exposing the piece. Another way of seeing it is that
1. Rh5+ levies a direct attack against the king and a half-attack against the queen (we say a player has a half-attack against a piece if an extra move would allow him to directly attack said piece). Kings must deal with direct attacks immediately, and the tempo Black loses by doing so is equivalent to an extra move for White, which, in accordance with our half-attack theory, means that on White's turn, he is now directly attacking the queen, which he captures on move 2. There are limitations to heuristics, e.g. if the king could in some cases block a check instead of moving, but the intuition is still there.
So back to this problem: First I was thinking "well, there are 3 attackers and 2 defenders" but that doesn't really give much intuition because it's not the same square being attacked each move. Another idea was that there are three half-attacks on g8 by the queen and the rooks (and only two defenders), but I could create other examples where this is the case and White doesn't have any real tactic available to him.
What's the intuition for why this tactic exists? What heuristic would allow me to recognize this kind of position later?