Question

У Буратино 26 монет. Кот Базилио положил одну фальшивую и их стало 27. Известно, что фальшивая монета тяжелее обычной. За какое минимальное число взвешиваний можно определить фальшивую монету? Весы из двух чаш, показывают или равновесие, или в какой-то больше, а в какой меньше

Answer 1

Ответ:

Ответ на фото..........

Answer 2

Problem Analysis

We have 26 coins, one of which is fake and heavier than the rest. We need to determine the fake coin using a balance scale that can compare the weights of two groups of coins. We want to find the minimum number of weighings required to identify the fake coin.

Solution

To solve this problem, we can use a binary search approach. We start by dividing the 26 coins into two equal groups of 13 coins each. We then compare the weights of these two groups.

- If the weights are equal, the fake coin must be in the remaining 13 coins. We repeat the process with the remaining 13 coins, dividing them into two groups of 6 and 7 coins, and comparing their weights. - If one group is heavier, the fake coin must be in that group. We repeat the process with the heavier group, dividing it into two groups and comparing their weights. - We continue this process of dividing the groups in half and comparing their weights until we find the fake coin.

Since we are dividing the groups in half at each step, the number of weighings required can be determined by finding the minimum number of times we can divide 26 by 2 until we reach 1.

Let's calculate the number of weighings required:

26 / 2 = 13 13 / 2 = 6.5 (rounding up to 7) 7 / 2 = 3.5 (rounding up to 4) 4 / 2 = 2 2 / 2 = 1

It takes a minimum of 5 weighings to determine the fake coin.

Answer

The minimum number of weighings required to determine the fake coin among the 26 coins is 5.

Note: The solution assumes that the balance scale can compare the weights of two groups of coins and accurately determine which group is heavier.