you should try retrograde in compositions of your own.. Start with the rare squares on the board which would reduce king mobility in absence** of any other material. There are 2 categories of such.. (spoiler: corners and sides).
add a knight to further reduce mobility (don't worry about the king being elsewhere, go for the jugular, and retrograde after).
do you see escaping leaks for the opponent king (watch out later for stalemate, but your first sub-problem is mobility, if you can create stalemate by composition, you can find the mate by moves reordering.
leaks are there i can remember or guess. (foggy in concrete but sure in intuition). add a second night tweak.. can the king still escape? add the pawn.. you could start with pawn too.
you can get more understanding conscious and intutive by doing that by yourself, than having a one solution directed automatic tool... but opînions may differ.
I skip to the hard complication (perhaps more unusual, but still within everyone logic ability knowing the mobiltiy rules).
if you find the mate (and proper turn that does not make it PAT=STALE). then try to find legal positions antetior to that.
perhaps starting with pawn might make it easier.. i don't recall. i am giving you elements, not a rubik cube recipe. i would not have been able to remember or learn such thing anyway...
search google for retrograde analysis, but don't get lost (this is at the basis of endgame tablebases, but you don't want to learn chess from there, just be a tourist).
you might even be able to gets the patterns of positions that would not work along the way.. and might want to look again at full king initial mobilitiy situations, to find the cornering ratchets.. but there may not always be. so that is why you might need the pawn and king mess already staged.;.. (don't take the pawn).
you can skip all that stimulating mind flex (guess work) with post #6. or use it as hints when stuck. (did not check, but assume that given the effort put into making that study).
anyone can fix things i did not cover, given the approach, of teaching nature before bottom truth (i may also have been erring in pedagogy, but if i were in op shoes, i would have like someone given me some hints like that, no being in anybody else shoe, i share just in case). I think i did not cover well how to reduce a completely free king to some side or corner.. a skill useful in many other ending abstractions.
(yes not a legal position, who cares, we are in the training world, nothing says you can't do jokes seriously, or flex your thinking away from real game situations, the work to go to real games generalization of that controlled retrograde approach, would naturally emerge with real game experience connecting without even your awareness (most people do not hear the subconscious noise, having a good pre-frontal lobe filtering, others have to learn to deal with that, digressing, see i could not block that one). connecting real game to this exerces will happen without sweat, upon real game slow enough experience.
add a knight to further reduce mobility (don't worry about the king being elsewhere, go for the jugular, and retrograde after).
do you see escaping leaks for the opponent king (watch out later for stalemate, but your first sub-problem is mobility, if you can create stalemate by composition, you can find the mate by moves reordering.
leaks are there i can remember or guess. (foggy in concrete but sure in intuition). add a second night tweak.. can the king still escape? add the pawn.. you could start with pawn too.
you can get more understanding conscious and intutive by doing that by yourself, than having a one solution directed automatic tool... but opînions may differ.
I skip to the hard complication (perhaps more unusual, but still within everyone logic ability knowing the mobiltiy rules).
if you find the mate (and proper turn that does not make it PAT=STALE). then try to find legal positions antetior to that.
perhaps starting with pawn might make it easier.. i don't recall. i am giving you elements, not a rubik cube recipe. i would not have been able to remember or learn such thing anyway...
search google for retrograde analysis, but don't get lost (this is at the basis of endgame tablebases, but you don't want to learn chess from there, just be a tourist).
you might even be able to gets the patterns of positions that would not work along the way.. and might want to look again at full king initial mobilitiy situations, to find the cornering ratchets.. but there may not always be. so that is why you might need the pawn and king mess already staged.;.. (don't take the pawn).
you can skip all that stimulating mind flex (guess work) with post #6. or use it as hints when stuck. (did not check, but assume that given the effort put into making that study).
anyone can fix things i did not cover, given the approach, of teaching nature before bottom truth (i may also have been erring in pedagogy, but if i were in op shoes, i would have like someone given me some hints like that, no being in anybody else shoe, i share just in case). I think i did not cover well how to reduce a completely free king to some side or corner.. a skill useful in many other ending abstractions.
(yes not a legal position, who cares, we are in the training world, nothing says you can't do jokes seriously, or flex your thinking away from real game situations, the work to go to real games generalization of that controlled retrograde approach, would naturally emerge with real game experience connecting without even your awareness (most people do not hear the subconscious noise, having a good pre-frontal lobe filtering, others have to learn to deal with that, digressing, see i could not block that one). connecting real game to this exerces will happen without sweat, upon real game slow enough experience.