Soma cube puzzle

'Hidden void' Soma designs are among my favorites. It's fun to show them to people, not letting them know that there is a hidden void, and then seeing if they can reconstruct the design.

ObPuzzle: What's the maximum volume of hidden voids that one can create using the standard 7 Soma pieces? A hidden void can not be seen from the outside, but doesn't have to be cubical (i.e., a 1 by 1 by 2 void is allowed, as long as it is completely enclosed).

Spoiler to Carl G.'s problems...

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(Use a fixed-width font to view diagram)

A Soma 'tree' (solution to both 1 and the bonus puzzle):

xxx gge gde ddd xax aaf gxe bce xxx baf bff bcc

Solutions to these have already been posted, but here is another puzzle:

I got a Soma Cube with a 'cover' in which to build the cube. The cover consists of a 3x3 base and a top hollow piece with a hole in each of the five sides:

[fixed-width font required] . ,' '. ,' _ '. < (_) > '. ,' '. ,' O O '. ,' ,''. .''. < 'v' > '. ,' '. ,' 'v'

Can you build it inside the cover so that one small cube sticks out of each of the five holes? Extra bonus if it's possible to pick it all up by the top cube.

It's difficult to explain what I mean, so there are some pictures at http://puzzles.zzlevo.net/soma.html that illustrates what I mean.

Andreas

Here is one idea. I haven't given it much thought so there could be a trivial win for one side, or perhaps all games turn out to be draws when both players play decently.

Two players, each one has a set of the seven Soma pieces. The two sets should be distinguishable (e.g. one white and one black). Use a board with 6x6 squares where the size of each square matches the pieces (e.g. the 's' piece can be laid out on the board to exactly cover four squares).

The players alternate making moves. Each move can be done in one of two ways:

- A player can add a piece to the board; the piece must be in contact with the board, no part of it may be outside the board and there must not be any empty space below any part of the piece (e.g. the 's' piece can only be placed in an upright position if it rests on some other piece). The pieces must be aligned with the squares on the board.

- A player can remove one of his own pieces if no other piece rests on it.

When a player places his last piece on the board, the other player makes one more move and then the game is over. Each player gets as many points as the sum of the heights of all columns of which he owns the topmost piece. The player with most points wins.

If a player is not able to make a move when it's his turn (i.e. he is not able to place a piece and none of his pieces are removable) it's a draw. I don't know if this can happen - ObPuzzle: can it? If it turns out that it's easy to make this happen perhaps it should be a win or loss instead depending on if it's easy to make it happen for yourself or your opponent.

Andreas