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Консультация № 188677
19.01.2016, 12:44
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В трёх вершинах квадрата АВСД находятся три кузнечика: А, В, С. Они играют в чехарду, при этом, если кузнечик А прыгает через кузнечика В, то после прыжка он оказывается на той же прямой, на которой находились А и В до прыжка, и на том же расстоянии от В (но по другую сторону). Может ли после нескольких прыжков один из кузнечиков попасть в четвёртую вершину Д исходного квадрата?
В трёх вершинах квадрата АВСД находятся три кузнечика: А, В, С. Они играют в чехарду, при этом, если кузнечик А прыгает через кузнечика В, то после прыжка он оказывается на той же прямой, на которой находились А и В до прыжка, и на том же расстоянии от В (но по другую сторону). Может ли после нескольких прыжков один из кузнечиков попасть в четвёртую вершину Д исходного квадрата?
Обсуждение
19.01.2016, 13:23
общий
Адресаты:
Обозначим вершины квадрата координатами (0,0), (0,1) и (1,0), (1,1)
При указанных прыжках каждая из координат кузнечиков или остается неизменной, или изменяется в ту или иную сторону на четное число х
Следовательно, для каждого из кузнечиков будет свое сочетание четности (ч, ч) (ч, н) и (н, ч) . И они не совпадают с четностью четвертой вершины (н, н) .
19.01.2016, 13:29
общий
Адресаты:
Изящно! Слов нет! 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
19.01.2016, 13:53
общий
Адресаты:
Надо было указать о наличии решения по ссылке 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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