Rearranging Tiles
This painting is made from 12 different tiles:
If the tiles are all removed and replaced randomly (i.e. they can be rotated and/or moved to a different section of the 4x3 grid) how many different ways are there to rearrange the tiles?
Feel free to include only one significant digit.
Assumption: One arrangement consists of each of the 12 spaces above filled with one tile face up in one of four possible orientations (rotations). No turning tiles upside down.
Image credit: https://www.rods.com
The answer is 8E+15.
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1 solution
There are 12 ways to choose the first tile, and 4 ways it can be rotated, 11 ways to choose the second tile (once we've chosen the first), and again 4 ways it can be rotated... etc.
So, the total number of ways is given by:
N = 1 2 ! ⋅ 4 1 2 = 8 e 1 5