cylinder chess problem

I saw this in a facebook gruop. I can't find the solution? can you?

Bd6+, Ka8....

Well what then.

Of course it is easy to force a mate. But not in 3. Fairy-Max says mate in 4 is the best you can do (1. Bh6+ Kc8 2. Bf4 Kd8 3. Bg3 Kc8 4. Qc7#). Unless 'vertical cylinder' means something different from what I think.

For normal Chess it would be mate in 3.

I gave up after half an hour, and looked up the solution. Yes, the problem is a sound mate-in-3 on a vertical cylinder board. The mating configuration is amazing, and I wouldn't have guessed it in a million years. Solution in spoiler white text:

>1,Kf2! Ka8 2.Bd2 Kh8 3.Qh1, 1...Kc8 2.Bh2 Kd8 3.Qd1.<

Thanks to Rocky64 but surely we have an horizontal cylinder? The solid black lines made me think that the board was wrapped to join the ends of the lines together across which no piece could pass.  That also looks vertical to me...i.e. h8 is joined to a8 not h1!! TTC.

@ttconnor153 Not sure what you mean since we agree that the h-file is joined to the a-file, and the resulting cylinder is vertical like this:

Fairy-Max has apparently a bug. 

I don't think so. Do you see a forced mate in 3 when the a-file is joined to the h-file, then?

The 'solution' given by Rocky64 in the solution contains moves that assume wrapping from 1st to 8th rank (a horizontal cylinder). And even in that context it seems wrong; with good defense this would be a mate in 5 at best.

I dont see any moves in Rocky64's solution that assume a horizontal cylinder.

 Sorry, my bad. I thought Qh1 was only possible through the upper edge. So it seems you are right: Fairy-Max doesn't report the fastest mate. I have never seen anything like that before. After 1.Kf2 (wich it allows, so it must think it is legal) it does report 'mated in 2'. So there is an inconsistency here. I will examine that.

[Edit] The latest official Fairy-Max (5.0b) release seems to not have this problem: it does report mate in 3. Turns out I was first using an older version (4.8V), which furthermore might have been adapted to do something special for an experimental variant, which broke other variants.

White text below

Oh, the bishop only controls 2 squares.

I reasoned that the usual mate patterns were impossible in 3, and also reasoned the cute pattern you'd see if the starting position had a queen on f3 and bishop on f4 was impossible in 3. Also, of course, it can't be in the middle of the board, it has to be on the edge.

So I was trying to figure out what kind of arrangement would give mate. I gave up and looked at the answer.

I missed that a queen on the a or h rank always controls 4 squares at the opposite end. I suspect this is was the key thing the composer noticed. After that you compose it so the mate happens in the corner like that for aesthetics.

Very nice.

Look at the quote plz.

Very nice indeed. The way the WQ controls those squares on the other side of the board made me wonder about the mobility of the Q on different squares in this kind of board. Because of the "absolute" vertical symmetry on a vertical cylinder, it's obvious that starting the Q on different squares on the same rank would make no difference to how many squares it controls.  So I tested varying the starting ranks of the piece, and to my surprise, that made no difference either! What this means is, on an open vertical cylinder board, no matter which of the 64 squares you place the Q, it controls the exact same number of squares - 27, Two sample diagrams:

Well, the rook movements of the queen being the same no matter where it is placed should be no surprise. And making the board a cylinder makes all diagonals equally long as the ranks and files. So with this mind it makes sense the queen has access to the same amount of squares on an empty board regardless of position.

The solution was really nice, I was not able to solve this one. 

That'd be weird. What if the cylinder chess was 4D? (Quote to answer)