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Консультация № 179547
20.07.2010, 15:40
0.00 руб.
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На острове живут 100 рыцарей и 100 лжецов, у каждого из них есть хотя бы один друг. Рыцари всегда говорят правду, а лжецы всегда лгут. Однаждый утром каждый житель произнес либо фразу "Все мои друзья - рыцари", либо фразу "Все мои друзья - лжецы", причем каждую из фраз произнесли ровно 100 человек. Найдите наименьшее возможное число пар дружей, один из которых рыцарь, а другой лжец.
Обсуждение
Неизвестный
20.07.2010, 19:12
общий
это ответ
Здравствуйте, Гаряка Асмик.
1. Ни один рыцарь не может одновременно иметь в друзьях и рыцаря, и лжеца (т.к. в этом случае он не смог бы произнести ни одну из заданных фраз).
2. Если бы не было ни одной пары "Р-Л", то тогда бы все рыцари дружили только с рыцарями, а все лжецы - только с лжецами. Но в этом случае каждый бы житель заявил, что все их друзья - рыцари. Поэтому хотя бы одна пара друзей вида "Р-Л" существует.
3. Пары друзей "Р-Р" и "Л-Л" должны произнести дважды "все мои друзья - рыцари"
4. Фразу "все мои друзья лжецы" может произнести только пара "Р-Л"
Поэтому минимальное число пар друзей, в которых один рыцарь, а другой лжец, равно половине от произнесенных "все мои друзья - лжецы", т.е. 100/2=50 пар.
1. Ни один рыцарь не может одновременно иметь в друзьях и рыцаря, и лжеца (т.к. в этом случае он не смог бы произнести ни одну из заданных фраз).
2. Если бы не было ни одной пары "Р-Л", то тогда бы все рыцари дружили только с рыцарями, а все лжецы - только с лжецами. Но в этом случае каждый бы житель заявил, что все их друзья - рыцари. Поэтому хотя бы одна пара друзей вида "Р-Л" существует.
3. Пары друзей "Р-Р" и "Л-Л" должны произнести дважды "все мои друзья - рыцари"
4. Фразу "все мои друзья лжецы" может произнести только пара "Р-Л"
Поэтому минимальное число пар друзей, в которых один рыцарь, а другой лжец, равно половине от произнесенных "все мои друзья - лжецы", т.е. 100/2=50 пар.
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