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42: 3 L-pentacubes, 3 L4-pentacubes
1 solution for K, 2 solutions for F, 3 solutions for B, 3 solutions for C, 3 solutions for E, 3 solutions for G, 3 solutions for H, 4 solutions for A, 6 solutions for D and 7 solutions for J

3×   3×

empty dicube at K
empty dicube at F
(1 of 2)
empty dicube at F
(2 of 2)
empty dicube at B
(1 of 3)
empty dicube at B
(2 of 3)

empty dicube at B
(3 of 3)
empty dicube at C
(1 of 3)
empty dicube at C
(2 of 3)
empty dicube at C
(3 of 3)
empty dicube at E
(1 of 3)

empty dicube at E
(2 of 3)
empty dicube at E
(3 of 3)
empty dicube at G
(1 of 3)
empty dicube at G
(2 of 3)
empty dicube at G
(3 of 3)

empty dicube at H
(1 of 3)
empty dicube at H
(2 of 3)
empty dicube at H
(3 of 3)