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
  • Quadruples
  • Quintuples
  • Sextuples
  • Septuple
  • Pairs

    4I-4K84K-4N24L-4T2
    4I-4L24K-4Q64N-4Q4
    4I-4N44K-4S24N-4S2
    4I-4Q64K-4T24N-4T2
    4I-4S34L-4N24Q-4S3
    4I-4T44L-4Q24Q-4T8
    4K-4L44L-4S24S-4T2

    Triples

    4I-4K-4L8 4I-4L-4S4 4I-4S-4T4 4K-4N-4T4 4L-4Q-4S3
    4I-4K-4N8 4I-4L-4T4 4K-4L-4N4 4K-4Q-4S2 4L-4Q-4T4
    4I-4K-4Q? 4I-4N-4Q? 4K-4L-4Q6 4K-4Q-4T8 4L-4S-4T2
    4I-4K-4S4 4I-4N-4S6 4K-4L-4S2 4K-4S-4T6 4N-4Q-4S2
    4I-4K-4T16 4I-4N-4T2 4K-4L-4T6 4L-4N-4Q4 4N-4Q-4T8
    4I-4L-4N6 4I-4Q-4S10 4K-4N-4Q6 4L-4N-4S4 4N-4S-4T4
    4I-4L-4Q2 4I-4Q-4T? 4K-4N-4S2 4L-4N-4T2 4Q-4S-4T8

    Quadruples

    4I-4K-4L-4N8 4I-4K-4Q-4S? 4I-4L-4Q-4T4 4K-4L-4N-4S4 4K-4N-4S-4T4
    4I-4K-4L-4Q16 4I-4K-4Q-4T? 4I-4L-4S-4T6 4K-4L-4N-4T4 4K-4Q-4S-4T8
    4I-4K-4L-4S8 4I-4K-4S-4T8 4I-4N-4Q-4S? 4K-4L-4Q-4S4 4L-4N-4Q-4S4
    4I-4K-4L-4T16 4I-4L-4N-4Q6 4I-4N-4Q-4T? 4K-4L-4Q-4T6 4L-4N-4Q-4T6
    4I-4K-4N-4Q? 4I-4L-4N-4S6 4I-4N-4S-4T4 4K-4L-4S-4T4 4L-4N-4S-4T4
    4I-4K-4N-4S8 4I-4L-4N-4T4 4I-4Q-4S-4T? 4K-4N-4Q-4S4 4L-4Q-4S-4T4
    4I-4K-4N-4T4 4I-4L-4Q-4S4 4K-4L-4N-4Q6 4K-4N-4Q-4T? 4N-4Q-4S-4T4

    Quintuples

    4I-4K-4L-4N-4Q? 4I-4K-4N-4Q-4T? 4I-4N-4Q-4S-4T?
    4I-4K-4L-4N-4S8 4I-4K-4N-4S-4T8 4K-4L-4N-4Q-4S4
    4I-4K-4L-4N-4T8 4I-4K-4Q-4S-4T? 4K-4L-4N-4Q-4T8
    4I-4K-4L-4Q-4S4 4I-4L-4N-4Q-4S4 4K-4L-4N-4S-4T4
    4I-4K-4L-4Q-4T? 4I-4L-4N-4Q-4T8 4K-4L-4Q-4S-4T4
    4I-4K-4L-4S-4T8 4I-4L-4N-4S-4T4 4K-4N-4Q-4S-4T24
    4I-4K-4N-4Q-4S? 4I-4L-4Q-4S-4T8 4L-4N-4Q-4S-4T8

    Sextuples

    4I-4K-4L-4N-4Q-4S8
    4I-4K-4L-4N-4Q-4T?
    4I-4K-4L-4N-4S-4T8
    4I-4K-4L-4Q-4S-4T8
    4I-4K-4N-4Q-4S-4T?
    4I-4L-4N-4Q-4S-4T4
    4K-4L-4N-4Q-4S-4T4

    Septuple

    4I-4K-4L-4N-4Q-4S-4T8

    Last revised 2015-11-22.


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    Col. George Sicherman [ HOME | MAIL ]