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288: 3 bulldozer-heptacubes, 3 cleaver-heptacubes, 3 dove-heptacubes
3 solutions for C, 8 solutions for A and many solutions for B

  3×   3×

empty cube at C
(1 of 3)

empty cube at C
(2 of 3)

empty cube at C
(3 of 3)