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H. G. Muller wrote on 2013-09-07 UTC
Note that it might be possible to interpose on a discovered check where ech King is checked by a different piece when the pieces are sliders, and their check rays intersect. E.g.

8/2pkkr2/r7/8/8/4P3/3B4/3RK3 w - - 0 1

1. Bb4++ Rad6!

In fact there is more. The methods for evading each check are limited to capture of the checker, interposition or King withdrawal. So with two checks there are 3x3=9 combinations of these, but only 6 combinations are different. You cannot capture two pieces in one move, or withdraw two Kings in one move, but as shown above you can sometimes block two sliders with one move. The 'inhomogeneous' possibilities are capture+withdrawal, interposition+withdrawal and capture+interposition. Now the latter is not possible with replacement capture, as interposition has to be on an empty square. The only capture in Chess that does that would be e.p. capture, but it turns out that the required preceding double-push can never create the discovered duple check that could be solved this way (because the pawn comes from a different square than its e.p.-capturer will end up on (*)).

Interposition+withdrawal is not possible, as a King cannot be used to interpose. (This is not Chinese Chess, and there are no Cannons...) But capture+withdrawal is perfectly possible:

8/2p2r2/r7/4k3/8/3kP3/3B4/3RK3 w - - 0 1

1 Bc3++ Kxc3!

*) I guess you could do this when one of the checking pieces would be a Moa-rider, as a Moa-rider on d1 can be blocked on both e2 and e3, so after 1. e2-e4 to check Kings on d5 and (discovered) g7 1... dxe3! would save the day.

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