Question

Вася живет в 14-этажном доме. На первом этаже живут всего два человека, с каждым этажом количество жильцов, которые пользуются лифтом, увеличивается на 4. Какую кнопку в лифте этого дома нажимают чаще всего?

Answer 1

чаще всего в лифте нажимают кнопку 1 этажа

Answer 2

Кнопка 1 этажа. Элементарно.

Answer 3

Answer in detail. Vasya lives in a 14-story building. On the first floor, there are only two people, and with each floor, the number of residents who use the elevator increases by 4. Which button in the elevator of this house is pressed most often?

To answer this question, we need to find out how many times each button is pressed by the residents of the building. We can assume that each resident uses the elevator twice a day, once to go down and once to go up. We can also ignore the button for the first floor, since no one needs to press it to go down.

Let's denote the number of residents on the i-th floor by n_i, and the number of times the button for the i-th floor is pressed by b_i. Then we have:

n_1 = 2 n_2 = 2 + 4 = 6 n_3 = 6 + 4 = 10 ... n_14 = 54 + 4 = 58

b_1 = 0 (no one presses the button for the first floor) b_2 = n_2 * 2 = 12 (6 residents press the button twice a day) b_3 = n_3 * 2 = 20 (10 residents press the button twice a day) ... b_14 = n_14 * 2 = 116 (58 residents press the button twice a day)

The button that is pressed most often is the one that has the largest value of b_i. We can compare the values of b_i for each floor and find the maximum. Alternatively, we can use a formula to calculate the value of b_i for any floor i:

b_i = (2 + 4 * (i - 1)) * 2 = 4 * i + 4

This formula shows that b_i increases by 4 for each floor, so the higher the floor, the more times the button is pressed. Therefore, the button that is pressed most often is the one for the highest floor, which is the 14th floor.

The answer is: the button for the 14th floor is pressed most often in the elevator of this house.