Question

Все участники фестиваля Чисел встали в круг и стали называть подряд идущие числа. Оказалось, что сумма номеров, названных на втором круге большесуммы номеров на первом круге, на 144. Сколько участников было на фестивале Чисел?

Answer 1

Ответ:

12

Пошаговое объяснение:

12

Answer 2

To solve this problem, we need to find the number of participants in the festival of numbers. Let's break down the information given:

- All participants stood in a circle and started naming consecutive numbers. - The sum of the numbers named in the second round was greater than the sum of the numbers named in the first round by 144.

To find the number of participants, we can use a mathematical approach. Let's assume there were n participants in the festival.

First Round:

In the first round, each participant would have named a number from 1 to n.

The sum of the numbers named in the first round can be calculated using the formula for the sum of an arithmetic series:

Sum of first round = (n/2) * (1 + n)

Second Round:

In the second round, the participants would have started naming numbers from 1 again, but this time, the numbering would have continued from where it left off in the first round.

The sum of the numbers named in the second round can also be calculated using the formula for the sum of an arithmetic series:

Sum of second round = (n/2) * (1 + n) + (n/2) * (1 + n)

Given Information:

According to the given information, the sum of the numbers named in the second round is greater than the sum of the numbers named in the first round by 144:

Sum of second round - Sum of first round = 144

Substituting the formulas for the sums of the rounds:

[(n/2) * (1 + n) + (n/2) * (1 + n)] - [(n/2) * (1 + n)] = 144

Simplifying the equation:

(n/2) * (1 + n) = 144

Now, let's solve this equation to find the value of n, which represents the number of participants in the festival.

Solving the Equation:

Expanding the equation:

(n^2 + n) / 2 - (n^2 / 2) = 144

Simplifying further:

n = 144 * 2

n = 288

Therefore, there were 288 participants in the festival of numbers.