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David Paulowich wrote on Sun, Oct 14, 2007 03:59 PM UTC:

'You know, the thought occurred to me that if the characteristics of pieces changed when they fuse or fission, then check could be given by a piece that was part of a compound that could not give check...' - Joe Joyce [2007-10-10]

This comment, raises some interesting possibilities. In the following diagram [White] has Rook+Nightrider compound (h8), Bishop (h1), King (b1). [Black] has King (a8), Rook (b7). Splitting the Nightrider off by moving h8-b5 blocks the check by the Rook (b7) and checkmates with the Rook (h8).

k . . . . . . X
. r . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . . 
. . . . . . . .
. K . . . . . B