Triominos

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Take a set of 24 triominos (dominos with three sides, a number at each
corner), consisting of all possible configurations
of the values 0, 1, 2, and 3, and place them into a hexagon, two units
on a side, such that each adjacent side matches correctly. Or, show why
it can't be done.
(Note that 1-2-3 is a different triomino than 1-3-2, since neither can be rotated to create the other; while 1-1-2 would be the same as 1-2-1, since the latter can be rotated to obtain the former.) |

Here is a list of the 24 triminos, numbered clockwise:

a. 0-0-0 | b. 0-0-1 | c. 0-1-1 | d. 1-1-1 | e. 0-0-2 | f. 0-2-2 |

g. 2-2-2 | h. 0-0-3 | i. 0-3-3 | j. 3-3-3 | k. 1-1-2 | l. 1-2-2 |

m. 1-1-3 | n. 1-3-3 | o. 2-2-3 | p. 2-3-3 | q. 0-1-2 | r. 0-2-1 |

s. 0-1-3 | t. 0-3-1 | u. 0-2-3 | v. 0-3-2 | w. 1-2-3 | x. 1-3-2 |

Source: Original.

Solution

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