Endgame study for Pion15

I found the task interesting and came up with a fairly simple solution:

Yes nice one. 

Bxe6 forces mate in two.

Starting with Nb3+ and going back with Nc1+  you can give mate in four (also in six, but not in eight cause then it would be repeating moves)

Can you fix mine above as well?

There are many solutions. Both of yours are good. Here is one I found. In this one, can you force mate in 5?

Correction. Pion15's position doesn't work.  1. h7+ Kf8  2. Bd6+ Ke8  3. h8=Q#

1. Nc6+ Ka8

2. Na7 Kb8

3. Bc8 Ka8

4. Bb7 Kb8

5. Nc6#

The same pieces in starting position is an endgame which must be done in the 50-move agreement. (i do not know how they call that in English). It is one of the most difficult endgames, which theoratically can be finished. I believe it can be done in 35 moves, but i am not sure about that number.

After 1. h7+ comes Kh8

Your mate in 5 is good, one of several. It means that in my position, White can force mate in any specified number of moves except 1 or 3. (The game will end by 50-move rule before there's a triple occurrence of position.)

The ending bishop and knight against king can be won from any starting position in 33 moves or less. I have practiced it a lot but only got to use it in a game one time.

I made up another task which is very hard, but you may like to think about it. I'll give it in my next comment.

The task required mate in 3 to be impossible, but my moves show that it is possible. White doesn't have to force mate in 3 to disqualify the position.

For this task, I need to explain what I mean by an "only" move. If a player has a choice of moves, and only one of them (ignoring  repetitions) does not change the evaluation of the position, it is an "only" move. So if White is winning and every move except one either draws or loses or repeats, that one is an "only" move. If White is drawing, and every move except one either loses or repeats, that one is an "only" move.

The task is to construct a position in which the first 12 half-moves are "only" moves for BOTH sides. It starts as a drawn position, with White to move. White has only one move to hold the draw. Then Black has only one move to hold a draw. Then White has only one move to hold a draw, and so on for the first 12 half-moves.

Why 12?  Because I have found a position in which the first 11 half-moves are "only" moves for both sides, and I want to know if that number can be increased. If you want to work on this, you may want to practice with a smaller number of consecutive "only" moves.

In the first reaction, then indeed my puzzle was false. I had ruled out mate in 3, only if it was forced.

About the second reaction. I would like to give that a try. That really is gonna take some time. Now i am going to sleep. It is 0:35 here and my alarm says goodmorning at 5:00

That task is hard, and you may not want to work on it steadily, so here is another endgame to solve.

White to play and win.

Does not matter if it is difficult, it will only take me more time and effort. Worst case scenario is I do not find the right moves. No one has ever won a match by giving up. ... For the endgame: 1. Kb4

1. Kb4 Kb2

2. c5

2. c5 Kc2

3. Kc4

3. Kc4 c6

4. Kd4