Suppose you have ten 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 × 5 grid. WebAssign Plot 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.) Incorrect: Your answer is incorrect.
+23245 My guess is this:
Since you have 10 places to put the 10 different squares, you have a total of
10x9x8x7x6x5x4x3x2x1 or 10! ways of doing this.
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 is: 10! / 2 / 2 / 2 or 10! / 8.
+23245 My guess is this:
Since you have 10 places to put the 10 different squares, you have a total of
10x9x8x7x6x5x4x3x2x1 or 10! ways of doing this.
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 is: 10! / 2 / 2 / 2 or 10! / 8.
