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Возраст сыновей

Двое друзей сидят на лавочке в парке. Вот их разговор.
Первый:
- У меня есть два сына.
Второй:
- Взрослые?
Первый (подумав):
- Еще дошколята. Произведение их возрастов равно количеству голубей около этой скамейки
Второй (после раздумий):
- Этих условий маловато для определения
Первый:
- Старший похож на мать
Второй: Теперь я знаю, по сколько каждому лет
Какого возраста сыновья у первого?
P.S. Условий в загадке достаточно, чтобы точно определить возраст сыновей. Не спешите смотреть ответ :)

Ответ: 4 года и 1 год
1. Второму недостаточно условий от первого, значит у второго получилось более одного варианта возрастов дошколят
2. Ответ первого про старшего убрал лишние варианты возрастов. Значит, один из вариантов был такой, что они ровесники (одинаковый возраст).
3. Рассмотрим, какие могли быть варианты "ровесников": 1 и 1, 2 и 2, 3 и 3, 4 и 4, 5 и 5, 6 и 6
Методом исключения:
- 6 и 6 не подходит, так как произведение их = 36. Тогда возраст детей останется либо 4 и 9, либо 2 и 18, либо 3 и 12, либо 1 и 36. Под дошколят никак.
- так же исключим 5 и 5, 4 и 4, 3 и 3
- 1 и 1 исключаем, так как они не ровесники
Осталось 2 и 2, что в произведении = 4.
Так как они не ровесники, то единственный вариант, который остался: 4 года и 1 год.
У скамейки гуляло 4 голубя :)
- (наведите курсор)

Добавил: Михаил
Источник: Друг


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