# A mobility puzzle

``````[FEN "8/8/8/8/pp6/kp6/1p6/1K6 w KQkq - 0 1"]
``````

This is a well-known position: both sides are stalemated (if it's their move). It's the lightest position with this property.

Devise the lightest positions where each piece of each side has exactly n moves. (So this would be n=0, you may go up to n=8, which is of course solved by putting only the kings into the free field.)

"Lightest" is defined in the standard way: first piece count, rather pawns than figures, rather black than white.

Experts, please hold you back, it's a very easy puzzle. :-)

It is true that for larger numbers of moves it becomes easier. From the following solutions, the ones from n=2 to n=8 are clearly optimal. The solution for n=1 looks good, but it may not be optimal.

### All pieces have 1 move

``````[FEN "8/8/8/1pp5/8/K7/8/k7 w - - 0 1"]
``````

### 2 moves (found by ghilesZ)

``````[FEN "2k5/K1p5/8/8/8/8/8/8 w - - 0 1"]
``````

### 3 moves

``````[FEN "8/8/8/8/8/8/K7/2k5 w KQkq - 0 1"]
``````

### 4 moves

``````[FEN "8/8/8/8/8/K7/8/2k5 w KQkq - 0 1"]
``````

### 5 moves

``````[FEN "8/8/8/8/8/K7/8/3k4 w KQkq - 0 1"]
``````

### 6 moves

``````[FEN "8/8/8/8/8/1K6/3k4/8 w KQkq - 0 1"]
``````

### 7 moves

``````[FEN "8/8/8/8/1K6/8/3k4/8 w KQkq - 0 1"]
``````

### 8 moves

``````[FEN "8/8/8/8/1K6/8/4k3/8 w KQkq - 0 1"]
``````
• I totally overlooked the 2 move with 3 pieces solution. Perfect! 1 move can also be done with 2 black pawns, but that is hardly a real improvement. Apr 17, 2021 at 8:30
• I think I've found a 3 unit solution for 2 moves: 8/8/8/8/8/8/k1P5/2K5 b - - 0 1. It is optimal as it can not be achieved with only 2 kings. Apr 17, 2021 at 11:41
• @HaukeReddmann I found the solution with 2 black pawns, which is better according to the given definition of "lightness", so I updated the answer.
– wimi
Apr 17, 2021 at 16:33
• @ghilesZ good find! I added it to the answer (or a symmetric one, because "rather black than white" according to the question).
– wimi
Apr 17, 2021 at 16:34
• @ghilesZ: And I overlooked that too...BTW, "rather black than white material" is sort of problem chess standard. Apr 17, 2021 at 20:51