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Сколько существует различных треугольников с целыми сторонами от 10 до 18?
У меня получилось 165 треугольников, это правильный ответ?
Решение было таким:
0) Неравенству треугольника удовлетворяют они все, так как сумма любых двух сторон не меньше 20, а любая сторона не больше 18.
1) Равносторонних треугольников ровно 9, со стороной от 10 до 18.
2) Если две стороны равны, а третья — другая, получаем 72 треугольника (9 способов выбрать две равные стороны и 8 способов выбрать третью, которая другая).
3) Разносторонних треугольников будет 3 из 9, то есть 84.
Итого получается 9+72+84=165.
А теперь вопрос: верны ли мои решение и ответ, и как можно сосчитать всё это побыстрее, чтобы не разбирать три различных случая?
Вы спрашивали "как можно сосчитать всё это побыстрее, чтобы не разбирать три различных случая?" - я полагаю, проще всего написать скрипт (некомпилируемую мини-программку) с алгоритмом :
Код:
Создать пустой массив M Для всех целых a от 10 до 18 Для всех целых b от 10 до 18 Для всех целых c от 10 до 18 Если (a+b > c) И (a+c > b) И (b+c > a) тогда Сообщить "Найден правильный треугольник" Создать новый элемент массива из чисел a, b, c в порядке возратания. Если такой элемент отсутствует в массиве, то добавить его в массив, как НЕповтор.
Количество элементов в массиве и будет числом треугольников. Если это число совпадёт с Вашим решением, значит, Ваше решение верно.
Если Вы ещё нуждаетесь в помощи решить Вашу задачу скриптом, Вы можете задать свой вопрос в раздел "JavaScript / VBScript Создание программ на языках JavaScript и VBScript" https://rfpro.ru/ask/651
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Тацечка и Кацечка 
