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It's possible to lose this game -- that is, there are starting arrangements from which it's impossible to get the knights to the other side. For an example, consider<p>
- B q K<br>
b r r b<br>
B R Q k<br>
N n n N<br>
<br>
In fact, the player cannot make any moves at all!
<p>I wonder if there are losing starting arrangements where the player has some moves available.