Занимательные задачи на логику

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Логические задачи предназначены, как для взрослых, так и детей. Подумайте хорошо и попробуйте разгадать их. Подобные задания тренируют память, развивают логику.

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  1. Доктор прописал человеку три таблетки, сказав, что он должен их принимать по одной через каждые полчаса. Через какое время после начала лечения человек выпьет самую последнюю — третью таблетку?
  2. Как число 66 увеличить в полтора раза, не производя над ним никаких арифметических действий?
  3. Самовар вмещает 30 стаканов воды. Один стакан наливается из полного самовара за полминуты. Следовательно, весь самовар при непрерывно открытом кране опорожнится за 15 минут. Верно ли это рассуждение? Если нет, то какая ошибка в нем допущена?
  4. Какая борона глубже разрыхлит землю — та, у которой 20 зубьев, или та, у которой их 60?
  5. Как двумя ударами топора разрубить подкову на шесть частей, не перемещая частей после удара?

 

ОТВЕТЫ:

  1. На первый взгляд может показаться, что человек выпьет последнюю таблетку через полтора часа, ведь это именно три раза по полчаса. На самом же деле он выпьет последнюю таблетку не через полтора часа, а через час. Представим себе, что он выпивает первую таблетку. Проходит полчаса. Он выпивает вторую таблетку. Проходит еще полчаса. Он выпивает третью таблетку. Стало быть, человек выпьет последнюю таблетку через час после начала лечения.
  2. Число 66 надо всего лишь перевернуть «вверх ногами». Получится 99, а это и есть 66, увеличенное в полтора раза.
  3. На первый взгляд кажется, что такое рассуждение совершенно верно: если один стакан наливается из полного самовара за полминуты, значит, все 30 стаканов выльются из него за 15 минут. Но это верно только в математическом отношении, а в данном случае речь идет о физическом явлении со своими закономерностями. Причем даже если ничего не знать о них, то все равно вполне понятно (даже на основе повседневного жизненного опыта), что свободно вытекающая (откуда угодно) вода выливается не с одной и той же скоростью, не равномерно. Сначала, когда некий резервуар полон водой, ее давление велико, и она вытекает быстрее. По мере опорожнения емкости давление воды в ней падает, и она начинает течь медленнее. Таким образом, первые стаканы воды выливаются из самовара под большим напором, а остальные — под меньшим, поэтому сначала стаканы наполняются быстрее, а потом медленнее. Следовательно, все 30 стаканов выльются из самовара при непрерывно открытом кране не за 15 минут, а за больший промежуток времени.
  4. Может показаться, что глубже разрыхлит землю борона с 60 зубьями. Однако это не так. Вспомним, что чем больше площадь опоры какого-либо тела, тем меньшее давление оно оказывает на находящуюся под этим телом поверхность. (По этой причине, например, идущий по снежному сугробу человек проваливается в него каждой ногой, а лыжник не проваливается, свободно скользя по его поверхности). У бороны с 60 зубьями площадь опоры больше, чем у бороны с 20 зубьями, значит, 60 зубьев с меньшей силой давят на землю, чем 20 зубьев. Значит, глубже разрыхлит землю борона с 20 зубьями.(См. также задачу 26.)
  5. Если начертить подкову в виде дугообразной линии, то разрезать ее двумя прямыми линиями более чем на пять частей не удастся. Если же нарисовать подкову такой, какова она на самом деле, т.е. имеющей ширину, то задача (может быть и не с первой попытки) является выполнимой.

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