I guess everyone know about how to play tetris. You rotate the puzzles and try to build a complete horizontal line and that line would disappear. The one who have less taller blocks would win the game.
Recently I found this game, tetris 3D.
It is not exactly like this, but pretty similar (source: http://downloadsoftwarestore.com/software/keyword/55555)
Oh yeah, I'm in love with something that have 3D interface. Basically, we have to rotate the puzzles in 3D axis and fill in the square surface. Later on I figure out that it is not that fun comparing with conventional 2D....so why?
That's because you are allowed to rotate the puzzles in 3 axis!
Let me explain to you. In 2D tetris, you have only one option to rotate your puzzles (CCW) to achieve all possible arrangement of 2D puzzle. Meanwhiles, in 3D tetris, you are allowed to rotate this 3D puzzles in 3 axis....I do some research, and I find out that we required only 2 axis of rotation for fully rotate the 3D puzzles in all possible arrangements!
Move to lower dimension puzzle, the 1D puzzle. There is only one possible shape of puzzle allowed in 1D, that is the line shape. Therefore, in this 1D tetris, you don't need any rotation to rotate it because the puzzle field would have only one dimension as well--the line field.
So I guess, you required 0 rotation for 1D puzzle. You required 1 rotation for 2D puzzles, and you required 2 rotations for 3D puzzles. And in general, we required n-1 rotations for n-Dimension puzzles. However, I really don't know how to test my hypothesis for more than 3D (and it would be fantastic to see it!)
I really don't know how to relate it with recent knowledge that I have. Maybe it is due to the degree of freedom because the formula is pretty similar (n-1). Anyway, please feel free to leave your discussion.
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