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I don't know if there is already name for this, but I like to call this type of puzzle an "onlymate": the only legal move delivers mate!
The challenge is not in the puzzle itself, but in the construction thereof. Can you create an onlymate?
Something a little different this time...
That last one is really nice.
But that's flawed!!! it's check but not check mate, the rook can take the bishop and there's a few pices able to block the bishop!!
No, it's a double check.
At first, I didn't understand your Frampits vs Totem puzzle as I thought, "It must be black's move and he can go ...Kh7 etc, Edit: or ...RxBe3 mate or ...QxBe3. Then I understood.
Clever. Hard to believe it is from a game.
here's two possibly devious cases!