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Don't know whether anyone will ever see this, but just wanted to say this is a great little game!  I saw it described on the Wikipedia under Chess Variants.  I found a not-very-good implementation of it in the Google Play store, and decided to write a better version so I could play it on the go.

I've found the corner-to-opposite-corner mode is a very quick game, while the full-board-tour is quite a bit longer and if you don't plan at least one move ahead you can easily get stuck.  It's a little unforgiving for younger players!

I played with different win conditions and decided these variants were my favourite:

- Visit all four corners, in whatever order you want

- Visit all border squares in sequence


External links appear to be allowed here, so I hope this isn't against the rules!  If you have an Android phone and want to play Queen's Quadrille, my app is available here: https://play.google.com/store/apps/details?id=com.maycontainsoftware.queensquadrille