Чаша с изумрудами

Есть горстка (например, 20, не столь важно число) изумрудов неправильной формы (неотделанные камни) и чаша с водой. Если в чашу опустить все изумруды, тогда уровень воды в чаше поднимется до краев и при попадании малейшей пылинки, хоть капля, но перельется через край.

Как только с помощью рук и головы (мозгов) выяснить, какой из изумрудов больше по объему? Никакого долива воды не предусмотрено

Ответ: Разделим изумруды попарно и проверять будет каждую пару на предмет наибольшего объема камня (одного из двух). Наибольшие откладывать в сторону. После того, как будут проверены все пары и отобраны наибольшие, уже их разбиваем на пары и снова проверяем попарно. И так до того, пока не останутся 2 самых объемных изумруда, из которых опять-таки отбирается наибольший, который и будет самым крупным.

Отбор же одного самого крупного из двух можно легко осуществить, если сначала вместе с рукой опустить один камень в чашу и опустить туда руку настолько, чтобы вода поднялась до предела краев, но не выливалась. Останется на руке след от границы воды, который не успеет высохнуть, пока камень вытаскиваем и кладем новый. Если после опускания второго камня рука, погружаемая в воду до момента поднятия воды до краев, будет выше границы, то второй камень меньше, если ниже, то второй крупнее.

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