Suppose you have six squares of stained glass, all of different colors, and you

Question

Suppose you have six 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 x 3 grid. How many different ways can you do this, taking symmetry into account? (Note that any pattern may be rotated 180 degree, flipped vertically, or flipped horizontally. You should count all the possible resulting patterns as the same window.

0/1 points | Previous Answers HunterDM2 4.3.018 My Notes Ask Your Teacher Suppose you have six 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 x 3 grid How many different ways can you do this, taking symmetry into account? (Note that any pattern may be rotated 180°, flipped vertically, or flipped horizontally. You should count all the possible resulting patterns as the same window.) 60

Explanation / Answer

However, for each choice, there is another choice which results in the same pattern, only rotated 180°; also, for each choice, there is another pattern flipped vertically; and, for each choice, there is another pattern flipped horizontally.

In each of these cases, divide the total number of patterns by 2, so, I believe, that the answer

6! / 2/2/2 = 90 try with this

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