Just to reply to Doug's comment from 11 years ago - no! I've been playing with the related game Queen's Quadrille recently, and there are many starting arrangements that are not possible to win from, and many that have some moves available.
For example, one moveable piece:
- R B ?
N N R B
B Q K ?
? ? ? ?
Two moveable pieces:
- Q B ?
K N R B
B R K ?
? B ? ?
In Queen's Quadrille I don't think it's possible to have three moveable pieces, as you can't connect four squares together without allowing a knight's move from next to one of the empty squares to a different empty square.
Going back to Hippodrome, however, the above layouts don't work because the knights are all at the bottom of the board. The failure starting positions in Queen's Quadrille depend on using knights in places where horizontal and diagonal movement is possible.
The only positions that start with an empty square next to a knight also have a different knight able to jump into that square - and in that situation there is *always* one piece in the middle that can move either horizontally or diagonally depending on the position of the knight, so there's no piece you can put there without it also being moveable.
I wrote an implementation of Hippodrome for Android with some alternative game modes. One of these was where the knights start in the middle four squares and need to be moved to the corners. It's an interesting mode that depends a lot on luck - it's possible to complete in just seven moves, but it requires a very specific starting arrangement. A side effect of the initial knight placement, however, is that it's dramatically less likely to start with an impossible position.
Just to reply to Doug's comment from 11 years ago - no! I've been playing with the related game Queen's Quadrille recently, and there are many starting arrangements that are not possible to win from, and many that have some moves available.
For example, one moveable piece:
- R B ?
N N R B
B Q K ?
? ? ? ?
Two moveable pieces:
- Q B ?
K N R B
B R K ?
? B ? ?
In Queen's Quadrille I don't think it's possible to have three moveable pieces, as you can't connect four squares together without allowing a knight's move from next to one of the empty squares to a different empty square.
Going back to Hippodrome, however, the above layouts don't work because the knights are all at the bottom of the board. The failure starting positions in Queen's Quadrille depend on using knights in places where horizontal and diagonal movement is possible.
The only positions that start with an empty square next to a knight also have a different knight able to jump into that square - and in that situation there is *always* one piece in the middle that can move either horizontally or diagonally depending on the position of the knight, so there's no piece you can put there without it also being moveable.
I wrote an implementation of Hippodrome for Android with some alternative game modes. One of these was where the knights start in the middle four squares and need to be moved to the corners. It's an interesting mode that depends a lot on luck - it's possible to complete in just seven moves, but it requires a very specific starting arrangement. A side effect of the initial knight placement, however, is that it's dramatically less likely to start with an impossible position.