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Twin Monarchs Chess Problems

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I've invented, or maybe just reinvented, a new kind of chess problem that is (I hope) immune to being solved by chess engines. It involves one or both sides having two kings!

Other than that, all the other rules of the game stay the same, so these problems still feel like normal chess problems. They just involve these two extra rules dealing with the new situations that can arise when you have two kings:

  1. The only way to checkmate a player is to checkmate both kings simultaneously.