Предмет: Математика, автор: amstep

На белой доске 5*5 Петя закрасил какие-то клетки синим цветом,а какие-то - красным (каждым цветом закрашена хотя бы одна клетка). Никакие две клетки красного и синего не имеют общей стороны. Какое наименьшее число клеток могло быть не закрашено?

Ответы

Автор ответа: mashablack

Всего клеток 25. Петя закрасил одним цветом минимум две клетки каждым цветом, допустим угловую и соседнюю клетку он закрасил синим. С этими клетками соприкасаются три клетки , тогда красным он сможет закрасить:25-2-3=20. Всего закрашено 20+2=22клетки.
2 случай:Если 1 клетка закрашена одним цветом, то с ней соприкасаются две клетки другого цвета. Можно закрасить 25-1-2=22. Всего закрашено 22+1=23.

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