How many ways to checkmate?


There are 0 ways to checkmate. The position is obviously illegal. Checkmate can only happen if the rules of the game are observed.
It's true that normal chess positions should be "legal" but there is a point where it is evident that a constructed position is intentionally "illegal". Now it is OK again, provided you treat it as a "fairy problem" which is a common category in chess compositions. This fairy type has no game history which has some consequences but not for this particular puzzle.
Chess problems are based on "ideas". It is considered a compositional weakness to express an idea in a fairy type when the same is achievable in standard chess. The "escape" into illegality is wholly unnecessary for the diagram puzzle. Here is a cleaned up diagram with some extra mates (another one exists with the exact same mates) - legal and most junk removed:
Here is an example of the difference between a "fairy" problem and a "standard" problem. The second diagram is illegal and is therefore of the fairy type. Illegal diagrams have no game history. Can you see why it could have 2 solutions while the first diagram only has 1?

There are 0 ways to checkmate. The position is obviously illegal. Checkmate can only happen if the rules of the game are observed.
It's true that normal chess positions should be "legal" but there is a point where it is evident that a constructed position is intentionally "illegal". Now it is OK again, provided you treat it as a "fairy problem" which is a common category in chess compositions. This fairy type has no game history which has some consequences but not for this particular puzzle.
Chess problems are based on "ideas". It is considered a compositional weakness to express an idea in a fairy type when the same is achievable in standard chess. The "escape" into illegality is wholly unnecessary for the diagram puzzle. Here is a cleaned up diagram with some extra mates (another one exists with the exact same mates) - legal and most junk removed:
Fairy problems generally state up front what the new rules are, rather than trying to sneak the rule change by the solver.
Requiring legal positions would severely limit some fairy forms, to be sure; e.g, there could not be Platzwechsel Circe problems with less than 32 units.
Given the recent surge in fairy retros, it is not always true that the history of the position doesn't matter.
In many Circe forms, rebirths of fairy pieces go to the promotion rank, because the piece is considered to have promoted previously from a normal pawn. This is clearly an eye pointing to the history of the position.

Here is an example of the difference between a "fairy" problem and a "standard" problem. The second diagram is illegal and is therefore of the fairy type. Illegal diagrams have no game history. Can you see why it could have 2 solutions while the first diagram only has 1?
I wouldn't call example #2 a fairy problem; I'd call it a "joke" problem. To me that is a separate genre, more for amusement and not to be taken as seriously.
I wouldn't call example #2 a fairy problem; I'd call it a "joke" problem. To me that is a separate genre, more for amusement and not to be taken as seriously.
It's OK to have that opinion. Then, I suppose you'd call post #1 also a joke problem. The relation between the diagrams in post #1 and post #7 is the same as between the diagrams of puzzle 2 and puzzle 1 in my last post. Or do you have an argument why it is not so?

I wouldn't call example #2 a fairy problem; I'd call it a "joke" problem. To me that is a separate genre, more for amusement and not to be taken as seriously.
It's OK to have that opinion. Then, I suppose you'd call post #1 also a joke problem. The relation between the diagrams in post #1 and post #7 is the same as between the diagrams of puzzle 2 and puzzle 1 in my last post. Or do you have an argument why it is not so?
I'm not sure I'd call #1 a joke problem, simply because the probability of any 'wit' is too low.
I'm not sure I'd call #1 a joke problem, simply because the probability of any 'wit' is too low.
I take that as a compliment for my puzzle 2. Thanks!

there are 17 ways:
6 with all the knights, and 11 with the queens
Well, looks like MynameisJeff21lol answered it correctly first!
there are 17 ways:
6 with all the knights, and 11 with the queens
Well, looks like MynameisJeff21lol answered it correctly first!
Did he? I count 7 mating moves with the knights which makes 18 mates alltogether.

there are 17 ways:
6 with all the knights, and 11 with the queens
Well, looks like MynameisJeff21lol answered it correctly first!
Did he? I count 7 mating moves with the knights which makes 18 mates alltogether.
I think he counted Nd8-f7 as a queen checkmate because it's actually a queen and knight checkmate
I think he counted Nd8-f7 as a queen checkmate because it's actually a queen and knight checkmate
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Probably, but it is the knight that moves! I miscounted one queen mate myself, Qg6-f6 is not mate. So alltogether there are 10 queen checkmates and 7 knight checkmates.