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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Сколькими способами можно рассадить трёх французов, трёх англичан и трёх русских за круглый стол так, чтобы никакие два человека одной национальности не сидели рядом, если считать рассадки, отличающиеся лишь поворотом, одинаковыми?
Пытался перебором, получил что если в тройках нац. не повторяются то таких вариантов 9, пробовал деревом, но очень все запутанно, пытался написать программу, что бы получить ответ хотя бы знать от чего отталкиваться, но не знаю как учесть перестановки по кругу. Помогите пожалуйста.
Кажется, все не так сложно, если сначала рассадить, например только французов, а потом добавлять остальных. Посмотрите, не упустил ли я что-нибудь.
Обозначим буквами A, B, C французов, англичан и русских. Будем расставлять буквы A, B, C в ряд так, чтобы, никакие две одинаковые не стояли рядом, а первая и последняя были разными. Размещения, которые получаются друг из друга кольцевым сдвигом, считаем одинаковыми. Сначала расставим три буквы A возможными способами, оставляя пустые места для B и C. Всего получается четыре способа размещения, показанные в таблице ниже. Они отличаются количеством пустых мест между буквами: 1-1-4, 1-2-3, 2-1-3, 2-2-2.
Обозначим буквами A, B, C французов, англичан и русских. Будем расставлять буквы A, B, C в ряд так, чтобы, никакие две одинаковые не стояли рядом, а первая и последняя были разными. Размещения, которые получаются друг из друга кольцевым сдвигом, считаем одинаковыми. Сначала расставим три буквы A возможными способами, оставляя пустые места для B и C. Всего получается четыре способа размещения, показанные в таблице ниже. Они отличаются количеством пустых мест между буквами: 1-1-4, 1-2-3, 2-1-3, 2-2-2.
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