题目
2025 penguins (675 each of emperors,kings and gentoos) stand in a line from left to right.They may move by performing the penguin shuffle in which an emperor takes a king’s place,a gentoo takes the position vacated by the emperor and the displaced king takes the place vacated by the gentoo. Prove that,no matter what the starting order,it is possible to place the emperors on the left,kings in the middle and gentoos on the right after a finite number of shuffles. 2025只企鹅(其中帝企鹅、王企鹅和金图企鹅各675只)从左到右站成一排。它们可以通过执行“企鹅换位”来进行移动：一只帝企鹅占据一只王企鹅的位置，一只金企鹅占据这只帝企鹅原来的位置，而被挤出的王企鹅则占据这只金图企鹅原来的位置。请证明无论初始排列顺序如何，通过有限次数的换位操作，可以将所有帝企鹅排在左边，所有王企鹅排在中间，所有金图企鹅排在右边。 ——、、、
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