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Count the ways... (Posted on 2005-10-28) Difficulty: 2 of 5
How many ways can you fit 8 identical 2 by 1 rectangles into a 4 by 4 square? Reflections and rotations count separately.

See The Solution Submitted by Tristan    
Rating: 4.0000 (2 votes)

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Solution by hand | Comment 4 of 6 |

for each retangle and orientation (vertical vs. horizontal), there are four positions counting rotations and reflections.  For each arrangement of rectangles in the square, there are 8! ways of creating it with 8 distinct rectangles.  The tricky part is to find the number of possible arrangements of 2x1 rectangles in a 4x4 square.  I count 36: 16 that quadrisect the square, 18 that only bisect it, and 2 that do neither.

Thus, the result is 4 * 8! * 36 = 5806080 possible arrangements. 

Hmm, guess i worked a  little too hard ;).

Edited on October 28, 2005, 5:55 pm
  Posted by Josh70679 on 2005-10-28 17:46:27

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