Question

В период военных учений было создано несколько командных пунктов, каждый из которых имел линию связи со всеми остальными. Сколько пунктов было создано, если линий связи было 120?

Answer 1

Пусть пунктов будет n.
Тогда у каждого будет по (n-1) линий связи, а всего их будет 
(n-1)+(n-2)+(n-3)+...+2+1+0, т.к. к каждому следующему пункту надо провести на одну линию меньше.
Значит, получается арифметическая прогрессия с d=-1, a1=n-1,an=0
Тогда сумма будет
Sn=(a1+an)*n/2 или
120=(n-1+0)*n/2
n^2-n=240
n^2-n-240=0
D=1+960=961
√D=√961=31
n1=(1+31)/2=16 - ответ
n2=(1-31)/2=-15 - не подходит, т.к. n>0

Answer 2

Number of Command Posts Created during Military Exercises

During the military exercises, several command posts were created, each of which had a line of communication with all the others. The question asks how many command posts were created if there were 120 communication lines.

Unfortunately, the provided search results do not directly answer this question. However, we can make an educated guess based on general knowledge of military practices.

In military exercises, command posts are typically established to coordinate and control the operations. These command posts serve as centralized locations where commanders and staff can make decisions and communicate with each other and subordinate units.

The number of command posts created during military exercises can vary depending on the scale and complexity of the exercises. It is not possible to determine the exact number of command posts created based solely on the information provided.

However, we can make an assumption that each command post would have at least one communication line with each of the other command posts. If there were 120 communication lines in total, it suggests that there were multiple command posts involved in the exercises.

To determine the exact number of command posts, we would need more specific information about the exercise scenario and the organization conducting the exercises.

In summary, based on the information provided, it is not possible to determine the exact number of command posts created during the military exercises. However, it can be inferred that there were multiple command posts involved.