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# squares

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The first square in a sequence of squares is in ABCD position. (We read the vertices by starting with the lower-left vertex, and going clockwise.)

Then, after rotating it 90 degrees clockwise, it is in DABC position.

Next, it is reflected over a central vertical line, ending in CBAD position.

If the pattern of alternately rotating and reflecting continues, what position will the 2007th square be in? Give your answer with lower left vertex first and the other vertices in clockwise order.

waffles  Oct 22, 2017
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B           C              A            B            B         A           C        B          B       C

1            →            2            →          3          →         4        →        1

A           D              D            C           C         D           D        A          A       D

Note that  every 4  "transformations"  gets us back to the original orientation

So.......

Dividing  2007 by 4...

We get a remainder of  3/4  which results in the 3rd orientation in the pattern, i.e.,