«Китайские кольца»

В каждом двоичном числе, имеющем предшественника в последовательности, есть только один разряд, изменившийся с 0 на 1. Позиция этого разряда (считая справа налево) дана в виде десятичного числа, указанного в скобках рядом с соответствующим двоичным числом. Но эти числа являются также номерами первых семи перекладываемых дисков. Это соответствие сохраняется на протяжении всей стандартной последовательности перемещений при решении задачи. Используя только произвольное двоичное число в этой последовательности, Т. Уолш с нашего факультета в Университете пров. Западный Онтарио при помощи компьютера может восстановить ситуацию, возникающую в ходе решения задачи на соответствующей данному двоичному числу стадии. Однако разработанный им алгоритм слишком громоздкий для того, чтобы его можно было привести в настоящей статье.

Теперь познакомим читателя с головоломкой «Китайские кольца» (см. рисунок внизу). Предмет головоломки состоит из длинной проволочной петли, прикрепленной к рукоятке, и набора колец, накинутых на петлю. Каждое кольцо при помощи металлических стержней свободно связано с деревянной пластинкой, расположенной под петлей. Стержень, соединяющий кольцо с деревянной пластинкой, проходит также через кольцо, расположенное позади данного (ближе к рукоятке), препятствуя тем самым его снятию с петли.

Задача заключается в том, чтобы

снять все кольца. Как и при решении задачи о башне, новичок может легко ошибиться. На рисунке показаны первые два шага на пути к решению задачи с пятью кольцами. Чтобы снять кольцо с петли, оттяните петлю назад насколько возможно, вплоть до стержня, расположенного непосредственно перед кольцом, которое вы хотите снять. Последнее можно повернуть вверх, так чтобы поднятая часть кольца перешла через дужку петли и сошла с нее. Оттянув теперь петлю вперед, кольцо можно наклонить в сторону, и оно выпадет из петли. По ходу решения головоломки часто требуется снова помещать кольца на петлю; в подобных случаях выполняется обратная процедура.

Попытки решить головоломку с китайскими кольцами связаны с той же обшей проблемой, которая возникает в задаче о башне. Периодически появляются «конфигурации», в которых то или иное число колец оказывается снятым с петли, и играющий надеется, что существует какая-то аналогичная последовательность перемещений, позволяющая решить задачу полностью — снять все кольца с петли.

 

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