Difference between revisions of "2008 iTest Problems/Problem 88"
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A six dimensional "cube" (a <math>6</math>-cube) has <math>64</math> vertices at the points <math>(\pm 3,\pm 3,\pm 3,\pm 3,\pm 3,\pm 3)</math>. This <math>6</math>-cube has <math>192\text{ 1-D}</math> edges and <math>240\text{ 2-D}</math> edges. This <math>6</math>-cube gets cut into <math>6^6=46656</math> smaller congruent "unit" <math>6</math>-cubes that are kept together in the tightly packaged form of the original <math>6</math>-cube so that the <math>46656</math> smaller <math>6</math>-cubes share <math>2-D</math> square faces with neighbors (<math>\textit{one}</math> <math>2</math>-D square face shared by <math>\textit{several}</math> unit <math>6</math>-cube neighbors). How many <math>2</math>-D squares are faces of one or more of the unit <math>6</math>-cubes? | A six dimensional "cube" (a <math>6</math>-cube) has <math>64</math> vertices at the points <math>(\pm 3,\pm 3,\pm 3,\pm 3,\pm 3,\pm 3)</math>. This <math>6</math>-cube has <math>192\text{ 1-D}</math> edges and <math>240\text{ 2-D}</math> edges. This <math>6</math>-cube gets cut into <math>6^6=46656</math> smaller congruent "unit" <math>6</math>-cubes that are kept together in the tightly packaged form of the original <math>6</math>-cube so that the <math>46656</math> smaller <math>6</math>-cubes share <math>2-D</math> square faces with neighbors (<math>\textit{one}</math> <math>2</math>-D square face shared by <math>\textit{several}</math> unit <math>6</math>-cube neighbors). How many <math>2</math>-D squares are faces of one or more of the unit <math>6</math>-cubes? | ||
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Latest revision as of 00:15, 19 July 2019
Problem
A six dimensional "cube" (a -cube) has
vertices at the points
. This
-cube has
edges and
edges. This
-cube gets cut into
smaller congruent "unit"
-cubes that are kept together in the tightly packaged form of the original
-cube so that the
smaller
-cubes share
square faces with neighbors (
-D square face shared by
unit
-cube neighbors). How many
-D squares are faces of one or more of the unit
-cubes?
Solution
<insert solution>