# Zucca's Challenge Problem for Tetracubes

A tetracube is a solid made of four cubes joined face to face. There are 7 tetracubes, not distinguishing reflections and rotations.

Zucca's Challenge Problem for Tetrominoes is: given a set of 2 or more tetrominoes, find a polyomino that can be tiled by each tetromino in the set, and none outside the set. Here I present results for the same challenge for tetracubes.

If you find a smaller solution or solve an unsolved case, please write.

• Pairs
• Triples
• Quintuples
• Sextuples
• Septuple
• ## Pairs

 4I-4K 8 4K-4N 2 4L-4T 2 4I-4L 2 4K-4Q 6 4N-4Q 4 4I-4N 4 4K-4S 2 4N-4S 2 4I-4Q 6 4K-4T 2 4N-4T 2 4I-4S 3 4L-4N 2 4Q-4S 3 4I-4T 4 4L-4Q 2 4Q-4T 8 4K-4L 4 4L-4S 2 4S-4T 2

## Triples

 4I-4K-4L 8 4I-4L-4S 4 4I-4S-4T 4 4K-4N-4T 4 4L-4Q-4S 3 4I-4K-4N 8 4I-4L-4T 4 4K-4L-4N 4 4K-4Q-4S 2 4L-4Q-4T 4 4I-4K-4Q ? 4I-4N-4Q ? 4K-4L-4Q 6 4K-4Q-4T 8 4L-4S-4T 2 4I-4K-4S 4 4I-4N-4S 6 4K-4L-4S 2 4K-4S-4T 6 4N-4Q-4S 2 4I-4K-4T 16 4I-4N-4T 2 4K-4L-4T 6 4L-4N-4Q 4 4N-4Q-4T 8 4I-4L-4N 6 4I-4Q-4S 10 4K-4N-4Q 6 4L-4N-4S 4 4N-4S-4T 4 4I-4L-4Q 2 4I-4Q-4T ? 4K-4N-4S 2 4L-4N-4T 2 4Q-4S-4T 8

 4I-4K-4L-4N 8 4I-4K-4Q-4S ? 4I-4L-4Q-4T 4 4K-4L-4N-4S 4 4K-4N-4S-4T 4 4I-4K-4L-4Q 16 4I-4K-4Q-4T ? 4I-4L-4S-4T 6 4K-4L-4N-4T 4 4K-4Q-4S-4T 8 4I-4K-4L-4S 8 4I-4K-4S-4T 8 4I-4N-4Q-4S ? 4K-4L-4Q-4S 4 4L-4N-4Q-4S 4 4I-4K-4L-4T 16 4I-4L-4N-4Q 6 4I-4N-4Q-4T ? 4K-4L-4Q-4T 6 4L-4N-4Q-4T 6 4I-4K-4N-4Q ? 4I-4L-4N-4S 6 4I-4N-4S-4T 4 4K-4L-4S-4T 4 4L-4N-4S-4T 4 4I-4K-4N-4S 8 4I-4L-4N-4T 4 4I-4Q-4S-4T ? 4K-4N-4Q-4S 4 4L-4Q-4S-4T 4 4I-4K-4N-4T 4 4I-4L-4Q-4S 4 4K-4L-4N-4Q 6 4K-4N-4Q-4T ? 4N-4Q-4S-4T 4

## Quintuples

 4I-4K-4L-4N-4Q ? 4I-4K-4N-4Q-4T ? 4I-4N-4Q-4S-4T ? 4I-4K-4L-4N-4S 8 4I-4K-4N-4S-4T 8 4K-4L-4N-4Q-4S 4 4I-4K-4L-4N-4T 8 4I-4K-4Q-4S-4T ? 4K-4L-4N-4Q-4T 8 4I-4K-4L-4Q-4S 4 4I-4L-4N-4Q-4S 4 4K-4L-4N-4S-4T 4 4I-4K-4L-4Q-4T ? 4I-4L-4N-4Q-4T 8 4K-4L-4Q-4S-4T 4 4I-4K-4L-4S-4T 8 4I-4L-4N-4S-4T 4 4K-4N-4Q-4S-4T 24 4I-4K-4N-4Q-4S ? 4I-4L-4Q-4S-4T 8 4L-4N-4Q-4S-4T 8

## Sextuples

 4I-4K-4L-4N-4Q-4S 8 4I-4K-4L-4N-4Q-4T ? 4I-4K-4L-4N-4S-4T 8 4I-4K-4L-4Q-4S-4T 8 4I-4K-4N-4Q-4S-4T ? 4I-4L-4N-4Q-4S-4T 4 4K-4L-4N-4Q-4S-4T 4

## Septuple

 4I-4K-4L-4N-4Q-4S-4T 8

Last revised 2015-11-22.

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Col. George Sicherman [ HOME | MAIL ]