What is the most complicated endgame

Yes, the solution is different if the position is different. I don't think anyone will disagree with that.

I agree that it is a win for white and Rb4+ is the first move.  My point is that it's not as simple as it looks. Depending on Black's moves, White has to triangulate, make delaying moves, avoid advancing a pawn prematurely, etc.

The example below is simplistic, and anyone familiar with the technique would not do this.  But, there are other, more subtle pitfalls that I encountered learning how to play  this endgame.  They usually occur as my pawns approached the fifth or sixth ranks.

My question now that I have learned the technique:  Will I remember it if this position occurs in one of my future games?  If I don't, I will probably make one of several stupid moves.

And illegal.

Maybe he making a push for cloning!

Oh really?! Now that you say it I guess it looks a little strange. It was stumping all of my students.

KxK

What does that tell us about how well your students have been taught?

Hey, rychessmaster1. I know a position that's a forced mate for White in 549 moves. Would you be interested in playing that one out? Of course, we would agree to disregard the 50-move rule.

No, that one was a mate in 545, not 549. The mate in 549 position is shown below. I'll play White. If you make the best moves for Black, I can't mate you in less than 549 moves. But we have to agree that I will win on the spot if you make a mistake that will let me mate sooner than move 500. I will start with 1.Kf5.

White to play and mate in 549.

1.Kf5 Rb5+ 2.Kg4

Let's see ... 1 single move per 2 hours, total 1100 single moves (rounded up). If one of you is unemployed and the other one is a pensioner, you can do this for 10 hours per day. Multiplying ... dividing .... takes us to 220 days!

What I am getting at is this. I need to do some supermarket shopping. Will you guarantee me that your exchanges won't be finished before I can take my place behind the screen again?

Well, I'm retired, so I guess that makes rychessmaster1 the unemployed one. But one bad move by Black could end it,  so you had better hurry with your shopping.

1.Kf5 Rb5+ 2.Kg4 Rb4+ 3.Kf3

1.Kf5 Rb5+ 2.Kg4 Rb4+ 3.Kf3 Nd7 4.Qh8+

Rychesssmaster1, I assume you've had your chess engine cranking away for the last 33 hours. What would you think about a time limit for each move? Eight hours should be OK, if you check for a new move just before going to bed.

1.Kf5 Rb5+ 2.Kg4 Rb4+ 3.Kf3 Nd7 4.Qh8+ Ke7 5.g7

KQKR or KBNK is not hard at all if you bother to study it, KRBKNN is really hard

1.Kf5 Rb5+ 2.Kg4 Rb4+ 3.Kf3 Nd7 4.Qh8+ Ke7 5.g7 Bf6 6.g8N+.

Your move wasn't made within the 8 hour time limit, but I'll give you a pass this once.

How about this one? I ran it through computer analysis and at various points we were both lost. The pieces prevailed but only just.