There are two distinct tricubes: three cubes in a straight row or three cubes forming an L shape.
There are 10 ways to form a set of 9 tricubes . Can all 10 possible sets be packed into a size 3 cube?
I think there is just one impossible case. 1L requires the 8 straights to leave an L gap. This is clearly impossible.
Here's how to do the rest:
0L is trivial.
Two L's can form a 3x2x1 block and so every even number is easy. That takes care of 2L, 4L, 6L, 8L.
Three L's can be stacked to make an Lshape 3 units high. The straights can easily fill the remainder. So that's 3L.
Combining the previous two ideas takes care of 5L and 7L.
9L almost got me, but it is possible:
433 453 899
122 455 889
112 667 677
This is interesting for its lack of symmetry.

Posted by Jer
on 20190112 10:43:41 