Занимательные задачи для интеллектуалов

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Если вы любите разгадывать разного рода головоломки, то эти задачки для вас. Занимательные задания разного уровня сложности. Подумайте хорошенько и решите их.

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1. Стандартный стакан (200 г) наполнен водой до краев. Сколько булавок можно в него накидать, чтобы из стакана не вылилось ни капли воды?

2. В коммунальной квартире жилец Иванов положил в общую плиту 3 полена своих дров, а жилец Сидоров — 5 поленьев. Жилец Петров, у которого не было своих дров, получил от обоих соседей разрешение приготовить свой обед на общем огне. В возмещение расходов он уплатил соседям 8 рублей. Каким образом они должны поделить между собой эту плату?

3. Миссионер попал в плен к дикарям, которые посадили его в темницу и сказали: «Отсюда только два выхода — один на свободу, другой к гибели; выбраться тебе помогут два воина, — один говорит всегда правду, другой всегда лжет, но неизвестно, кто из них лжец, а кто правдолюбец; ты можешь задать любому из них только один вопрос». Какой вопрос надо задать, чтобы выбраться на свободу?

4. Возможно ли вскипятить воду на открытом пламени в бумажной коробке?

5. На столе лежит в разложенном виде носовой платок. На нем в центре стоит горлышком вниз пустая стеклянная бутылка. Как вытянуть платок из-под бутылки, не прикасаясь к ней?

ОТВЕТЫ:

1. В стакан можно поместить более тысячи булавок. В этом случае ни капли воды из него не выльется, но над краями стакана образуется небольшая водяная выпуклость или «горка». По закону Архимеда тело, погруженное в воду, вытесняет объем воды, равный объему тела. Объем одной булавки настолько мал, что объем водяной «горки» над поверхностью стакана равен объему более тысячи булавок.

2. На первый взгляд кажется, что Иванов должен получить 3 руб., а Сидоров — 5 руб. Однако 8 руб. было уплачено не за 8 поленьев (по 1 руб. за полено), а только за третью часть от 8 поленьев, так как трое соседей пользовались огнем в одинаковой мере. Следовательно, 8 поленьев были оценены в 8 x 3 = 24 руб., и одно полено стоит 3 руб. Стало быть, Иванов за свои 3 полена должен получить 9 руб., но он сам воспользовался плитой на 8 руб., значит, ему причитается всего 9 — 8=1 руб.; а Сидоров за свои 5 поленьев должен получить 15 руб., но при вычитании из них 8 руб. за использование общей плиты ему остается 7 руб. Итак, из уплаченных Петровым 8 руб. Иванов должен взять себе 1 руб., а Сидоров — 7 руб.

3. Надо обратиться к любому из воинов со следующим вопросом: «Если я спрошу тебя, этот ли выход ведет на свободу, то ты ответишь мне «да»?» При такой постановке вопроса тот воин, который все время лжет, будет вынужден говорить правду. Допустим, вы, показывая ему на выход к свободе, говорите: «Если я спрошу тебя, этот ли выход ведет на свободу, то ты ответишь мне «да»?» Правдой в этом случае будет, если он ответит «нет», но ему ведь надо солгать и поэтому он вынужден сказать «да».

4. Вопрос задачи, на первый взгляд, кажется очень странным, ведь если держать бумагу над огнем, то она обязательно загорится. Но дело в том, что температура кипения воды намного ниже температуры воспламенения бумаги. Поскольку теплоту пламени забирает кипящая вода, бумага не может нагреться до нужной температуры и поэтому не загорается. Надо только, чтобы бумага была достаточно плотной, иначе вода просто порвет ее и выльется на пламя. Для кипячения воды вполне подойдет картонная коробка. То же самое объяснение лежит в основе такого явления, как несгораемая бумажка, плотно намотанная на металлический стержень (или стальной гвоздь) и внесенная в пламя свечи. Теплоту огня будет забирать стержень, не давая бумажке нагреться до нужной температуры и загореться.

5. Можно попытаться, используя инерцию бутылки, резким движением выдернуть платок из-под нее. Но, скорее всего, ничего не получится: положение бутылки слишком неустойчиво. Однако вспомним, что сила трения уменьшается при вибрациях. Кулаком одной руки надо равномерно и несильно стучать по столу недалеко от бутылки, а другой рукой — аккуратно тянуть платок. При определенной частоте и силе ударов по столу платок начнет плавно выскальзывать из-под бутылки. При этом важно обратить внимание на то, чтобы у края платка была не очень большая кромка: она, как правило, сбивает бутылку в последний момент. Поэтому лучше, чтобы платок вообще был без кромки.

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