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"en" .
"The 4-Color Cubes Puzzle" .
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"heidenwt@lafayette.edu" .
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"Starting with a palette of four colors, a 4-color cube is one where each face is colored\r\nwith exactly one color and each color appears on some face–there are a total of sixtyeight\r\ndistinct varieties of 4-color cubes. In the 4-Color Cube puzzle, one is given a\r\nset of 4-color cubes and tries to arrange a subset into a larger n×n×n 4-color cube.\r\nTo solve this puzzle, it is sufficient to fill in the large cube’s n-frame, its corners and\r\nedges. For each n we determine a minimal value, fr(n), so that given any arbitrary\r\ncollection of fr(n) 4-color cubes, there is always a subset which can be used to build\r\nan n-frame. In particular, we are able to show that for n ≥ 3, fr(n) = 12n − 16,\r\nthe smallest possible number. In addition, we describe a set of ten distinct 4-color\r\ncubes from which it is possible to build 2 × 2 × 2 frames modeled on all sixty-eight\r\ncolor cube varieties and conclude that this is the smallest size of such a set." .
"2022-01-06" .
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"2018" .
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"2022-01-06T19:27:36.984608224+00:00"^^ .
"Integers" .
"Natural Sciences" .
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"Lafayette College" .
"Berkove, E., A. Eickemeyer, and M. Schulman (2018) \"The 4-Color Cubes Puzzle.\" Integers 18: A68" .
"Eickemeyer, A." .
"Berkove, Ethan" .
"Schulman, M." .
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"Publication" .
"hdl:10385/0c483k66d" .
"noid:0c483k66d" .
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"2022-01-06T19:27:36.834769994+00:00"^^ .
"Mathematics" .
"Eickemeyer, A." .
"Berkove, Ethan" .
"Schulman, M." .
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"Article" .
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"ActiveFedora::Aggregation::ListSource" .
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