魔方比賽的打亂公式是如何產生的？

02-13

隨機生成的，不存在公式庫，並且相關隨機數產生器是密碼學安全的。

根據WCA規則，WCA打亂公式由官方提供的打亂程序生成。

4f) 比賽打亂序列必須使用當前官方版本的WCA打亂程序（見WCA官方網站）生成。

WCA的打亂程序是tnoodle，其源代碼在github上可以看到：thewca/tnoodle

從源代碼我們可以看到，對於每個項目，雖然各自的隨機生成演算法各異，但其生成的狀態都是由一個輸入的java.util.Random隨機數產生器來決定，並不額外引入其他隨機數。通過追溯該輸入，凡是用於生成狀態的隨機數產生器最終都是java.security.SecureRandom類的對象。從而這些隨機數產生器輸出的任何隨機數、隨機變數、隨機狀態的選取都是密碼學安全的。

4a) A scrambler applies scramble sequences to the puzzles.

4b) Puzzles must be scrambled using computer-generated random scramble sequences.

4b1) Generated scramble sequences must not be inspected before the competition, and must not be filtered or selected in any way by the WCA Delegate.

4b2) Scramble sequences for a round must be available only to the WCA Delegate and the scramblers for the event, until the end of the round. Exception: For Fewest Moves Solving, competitors receive scrambling sequences during the round (see Article E).

4b3) Specification for the scramble program: An official scramble sequence must produce a random state from those that require at least 2 moves to solve (equal probability for each state). The following additions/exceptions apply:

4b3a) For blindfolded events, the scramble sequence must orient the puzzle randomly (equal probability for each orientation).

4b3b) 2x2x2 Cube: The (random) state must require at least 4 moves to solve.

4b3c) Skewb: The (random) state must require at least 7 moves to solve.

4b3d) Square-1: The (random) state must require at least 11 moves to solve.

4b3e) 5x5x5 Cube, 6x6x6 Cube, 7x7x7 Cube, and Megaminx: sufficiently many random moves (instead of random state), at least 2 moves to solve.

4b3f) Pyraminx: The (random) state must require at least 6 moves to solve.

4b4) Each scramble sequence should be applied during a maximum time frame of 2 hours. This time frame starts when the scramble sequence is applied for the first time.

4d) Scrambling orientation:

4d1) NxNxN puzzles and Megaminx are scrambled starting with the white face (if not possible, then the lightest face) on top and the green face (if not possible, then the darkest adjacent face) on the front.

4d2) Pyraminx is scrambled starting with the yellow face (if not possible, then the lightest face) on bottom and the green face (if not possible, then the darkest adjacent face) on the front.

4d3) Square-1 is scrambled starting with the darker color on front (out of the 2 possible scrambling orientations).

4d4) Clock is scrambled starting with either side in front and 12 oclock pointing up.

4d5) Skewb is scrambled starting with the white face (if not possible, then the lightest face) on top and the green face (if not possible, then the darkest adjacent face) on the front-left.

4f) Competition scramble sequences must be generated using the current official version of the official WCA scramble program (available via the WCA website).

4g) After scrambling a puzzle, the scrambler must verify that the puzzle is scrambled correctly. If the puzzle state is wrong, the scrambler must correct it (e.g. by solving the puzzle and applying the scramble sequence again).

4g1) Exception: For the 6x6x6 Cube, 7x7x7 Cube, and Megaminx, it is not necessary to correct the puzzle state, at the discretion of the WCA Delegate.