This is an excellent topic. And these papers are fascinating. I've started referencing the possible number of tile side combinations in the reviews I've started, so its very useful to note the 24 combinations that are possible in the base game.Now I just need to do the math to figure out how many combinations are possible with added tile side types. I've done rough estimates, but they could we WAY off:Combinations on a 4-sided-tile given 3 tile side types: 24 (3 to the power of 4, or 81 total combinations, discarding the redundancies due to free rotation of tiles) Combinations on a 4-sided-tile given 4 tile side types: (4 to the power of 4, or 256 total combinations, discarding the redundancies due to free rotation of tiles)Combinations on a 4-sided-tile given 5 tile side types: (5 to the power of 4, or 625 total combinations, discarding the redundancies due to free rotation of tiles)Combinations on a 4-sided-tile given 4 tile side types: (6 to the power of 4, or 1296 total combinations, discarding the redundancies due to free rotation of tiles)

This is other link to "The math behind Carcassonne tiles"http://www.enworld.org/forum/showthread.php?216994-The-math-behind-Carcassonne-tiles

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