What is the pattern used to make all the Triominoes fit into one unit?
February 18, 2013 5:40 AM Subscribe
Never play Triominoes with a statistician. My partner and I played just a few games before she became obsessed with making all the pieces join, (match), together to form a whole unit. Is there diagram of how this is done? I would like to get back to playing the game. Thanks!
Best answer: I don't believe empath's link proves that it can't be done for the 56 triominoes in a branded game, in any shape; it only shows that there is no regular hexagonal solution for a set of 24 triominoes with the numbers 0-3, and for each set of three different numbers, there are two distinct triominoes, one labelled clockwise and one labelled counterclockwise.
The question at hand places no restrictions on the final shape as long as it is contiguous, and involves a branded game, using the numbers 0-5; it appears for branded games, for each set of three different numbers, there is only one triomino; on a bit of research, all the triominoes with three different numbers may or may not be oriented the same way (for the one analyzed at 23 skidoo's link, 18 of the 20 with three different numbers are oriented clockwise, and two counterclockwise). 23 skidoo's link places some interesting restrictions on what a solution would look like (including a number of edges which, it can be shown, must be present on the perimeter); a similar analysis could be carried out on other sets if they differed from the one described at that link, although the exact results may vary.
Here's a BGG thread describing an edition in which one tile has a counterclockwise configuration, and the consensus there seems to be that all tiles with three different numbers "should" have a clockwise configuration. Whether this is the case in your game, I don't know.
posted by DevilsAdvocate at 1:04 PM on February 18, 2013
The question at hand places no restrictions on the final shape as long as it is contiguous, and involves a branded game, using the numbers 0-5; it appears for branded games, for each set of three different numbers, there is only one triomino; on a bit of research, all the triominoes with three different numbers may or may not be oriented the same way (for the one analyzed at 23 skidoo's link, 18 of the 20 with three different numbers are oriented clockwise, and two counterclockwise). 23 skidoo's link places some interesting restrictions on what a solution would look like (including a number of edges which, it can be shown, must be present on the perimeter); a similar analysis could be carried out on other sets if they differed from the one described at that link, although the exact results may vary.
Here's a BGG thread describing an edition in which one tile has a counterclockwise configuration, and the consensus there seems to be that all tiles with three different numbers "should" have a clockwise configuration. Whether this is the case in your game, I don't know.
posted by DevilsAdvocate at 1:04 PM on February 18, 2013
Best answer: I've found a solution with a bit of trial and error plus some insight from the analysis at 23skidoo's link. It's not an elegant configuration, but it shows it can be done:
The parallelogram 1-0-0-4 at center left is not a typo; that's a "hole" in the configuration.
posted by DevilsAdvocate at 6:59 PM on February 18, 2013
5 3
/ \ / \
/ \ / B \
3-----1-----2-----4-----5
/ \ / \ / \ / \ /
/ \ / \ / \ / \ /
3-----1-----2-----2-----1 0-----1
\ / / \ / / \ / \
b \ / / \ / / \ / A \
2 1-----5 0-----4-----3
/ \ / \ / \ / \
/ \ / \ / \ / \
1-----1-----5-----5-----4-----4-----5-----2
a / \ / \ / \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \ / \ / \
4-----4 0-----5-----4 3-----3-----5-----4
\ / \ / \ / \ / \ / \
\ / \ / \ / \ / \ / \
2-----0-----0 3 3-----0
/ \ / / \ / \
/ \ / / \ / \
1-----1 1-----2-----3-----1
\ / \ /
\ / \ /
4-----0-----2-----3
\ / \ / \ /
\ / \ / \ /
3-----0-----5
\ /
\ /
2
The solution above is for what one might call the "canonical" set, where all triominoes with three numbers are numbered clockwise. For the set described in 23skidoo's link, where the 134 and 234 tiles are numbered counterclockwise, the above solution works with minor modification, by moving A to a and B to b.The parallelogram 1-0-0-4 at center left is not a typo; that's a "hole" in the configuration.
posted by DevilsAdvocate at 6:59 PM on February 18, 2013
This thread is closed to new comments.
posted by empath at 6:02 AM on February 18, 2013