Suppose you have eight squares of stained glass, all of different colors, and you would like to make a rectangular stained glass window in the shape of a 2 _ 4 grid.

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How many different ways can you do this, taking symmetry into account? (Note that any pattern may be rotated 180Á, flipped vertically, or flipped horizontally. You should count all the possible resulting patterns as the same window.)

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Computers and Technology

Cali

4 January, 03:31

Suppose you have eight squares of stained glass, all of different colors, and you would like to make a rectangular stained glass window in the shape of a 2 _ 4 grid.

WebAssign Plot

How many different ways can you do this, taking symmetry into account? (Note that any pattern may be rotated 180Á, flipped vertically, or flipped horizontally. You should count all the possible resulting patterns as the same window.)

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Natalie · Answer 1

It is easy to do since it can be rotated, these are something called circular permutations. Now, as it can be flipped, there's no difference between clockwise and counter-clockwise.

It's 8 tiles, all different, going around a rectangle.

That means is 7! / 2 = 2520 ways