Kenneth S. answered • 11/20/17
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Are all squares congruent?
Are these arrangements all supposed to be lined up (side by side)? Or are you allowing other arrangements such as 2 by 6, 3 by four?
On the face of it, since the word Combination is explicitly used, one might think 12C12 would be the answer--and that's ONE. Maybe it's 212 since there are two choices up/down) for 12 different squares.
My view is that this problem is not well written (too vague).
Kenneth S.
Possible configurations of squares:
A: one horizontal row of twelve
B: two horizontal rows of 6 each
C: three horizontal rows of 4 each
D: 4 horizontal rows of 3 each
E: 6 horizontal rows of 2 each
F: one vertical column, 12
In each case, the placements in the various slots by an
Arrangement of squares can be computed as 12P12, which is 12!
Arrangement of squares can be computed as 12P12, which is 12!
Furthermore, there are 4 orientations of each square (formed by rotations of 90o from whatever initial orientation applies).
(This is what you referred to as 4 tops.)
I believe that all these numbers must be multiplied to give the grand total of distinct-appearing configurations:
6•4•12! = 24(479001600) = 1.14960384 X 1010
Now that I understand the problem, after your clarifications (I think), it's an interesting one. Do you agree with this analysis?
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11/20/17
Rick R.
11/20/17