Покрытие доски 10×10

Докажите, что шахматную доску 10×10 нельзя покрыть фигурками следующего вида:

Покрытие шахматной доски 10x10

Ответ: Каждая фигурка указанного вида покрывает три клетки одного цвета и одну клетку другого (три клетки чёрного цвета и одну белого, либо наоборот). Поскольку всего на шахматной доске чёрных и белых клеток поровну, то количество фигурок, содержащих три белые клетки и одну чёрную, должно совпадать с количеством фигурок, содержащих три чёрные клетки и одну белую. Следовательно, общее количество фигурок должно быть чётным. Однако это невозможно, так как общее количество фигурок - 25.

Ваша оценка: Нет Средняя: 3.3 (787 оценки)


Комментарии

откуда это "так как общее количество фигурок - 25."?!

На доске всего 100 клеток, одна фигурка занимает 4 клетки. Вот и считай (с)

100? Не 64 клетки, нет?

Внимательно читать условие надо!!!

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В условии упоминание про шахматную доску вообще надо было убрать. Тогда решение с привлечением шахматной доски было бы чем-то особо гениальным. А так - прямо в условии даётся подсказка, что снижает уровень сложности интересной задачи. Так или иначе, не понятно, почему такими фигурками нельзя покрыть именно шахматную доску. А одноцветную, получается, можно, что ли?

привет всем~~~

Кстати шахматоую доску можно покрыт~~~

Минимальный площадь это 4х4~~~

Причем тут шахматная доска ..

А шашечный нельзя что ли ~ и причем тут разные цвета доски~~~

Любой прямоугольник со сторонами 4 m x 4n 

Можно покрыт булыжниками вот такой фигуры 

И жругого варианта на этом глобусе не может быть,,,,,

А что еси было 20 х10  то можно при таком мышлении,,,,,, неть и неть,,,(10 не=4m)

20x4можно,,,

А так при шахматном покраске доски (мысленно) можно конкретно для этого случая (если нет дрегих знании или ремеслов),

Что нечётное чисьло фигур никак не поместится ни какой площадье

Просто формулировка задачи не корекное 

((решение можно упоминуть  ,преставте под шахмат украшенную доску))####

Спосибо всем Вам .....

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В условии задачи не написано, что фигурки не могут накладываться. Не уточняется, что клетка фигурки соответствует клетке доски. Не написано, что каждая фигурка должна покрывать ровно четыре клетки доски.

Т.е. Вы хотите сказать, что доску допускается завалить "Т"-фигурками как листопадом, но при этом просится доказать, что это невозможно?

Условие задачи неточно. Да, без уточнений, получается, что доску покрыть фигурками можно. Даже и в один слой, но чтоб фигурки могли выступать за край доски.

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10×10 это не шахматная доска. А шахматную, покрыть такими фигурами можно.

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