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Really great image however I was confused by one comment on the page suggesting there are more than 892 variations. "I was confused at first because so many pa
by sparknlaunch12 14y ago
Really great image however I was confused by one comment on the page suggesting there are more than 892 variations.
"I was confused at first because so many partitions are not on the poster. I see that this poster has culled horizontal and vertical symmetries, but the entry is titled “the 892 unique ways to partition a 3×4 grid.” Given this, I think a poster with all 3,164 partitions would have been (counter intuitively) more elegant. Or if the poster had just been titled “892 unique ways to partition a 3×4 grid.”
- joejohnson 14y agoThere are 892 unique arrangements of unit rectangles in a 3x4 grid when you consider two arrangement which are rotations or mirror images of one another to be the same arrangement. When you count each arrangement and any rotations/mirror-images of that arrangement, there are 3,164 partitions. Example: This partition: +-+---+-+ | | | | | | +-+ | | | | | | +-+-----+ ...is just a rotation of this partition: +-+---+-+ | | | | | | +-+ | | | | | | +-+---+-+ There are 3,164 partitions if we say the above figures are distinct; if we call the above figures the same partition (but shown in two different orientations) then there are only 892 partitions.
- sparknlaunch12 14y agoThat makes sense. Thanks for the explanation.