Question

Вдоль дороги в стране Дураков растут 20 кустов, на каждом кусте по 9 монет. Прохожие должны срывать с каждого куста 22, 33 или 44 монеты, но при этом никто не должен срывать поровну монет с соседних кустов, иначе охранники арестуют нарушителя. Алиса, потом Буратино и после них Василио прошли вдоль дороги и сорвали все монеты. Алиса сорвала не менее 70 монет, а Буратино сорвал меньше всех. Сколько монет сорвал Василио?

Answer 1

33
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Answer 2

Problem Analysis

In this problem, there are 20 bushes along a road in the country of Durakov. Each bush has 9 coins. Passersby are supposed to pick 22, 33, or 44 coins from each bush, but they cannot pick an equal number of coins from neighboring bushes, as that would result in being arrested by the guards. Alice, Buratino, and Vasilio walked along the road and picked all the coins. Alice picked at least 70 coins, while Buratino picked fewer coins than anyone else. We need to determine how many coins Vasilio picked.

Solution

To solve this problem, we need to analyze the given information and make some deductions.

1. Alice picked at least 70 coins. 2. Buratino picked fewer coins than anyone else. 3. The number of coins picked from each bush must be 22, 33, or 44. 4. No two neighboring bushes can have the same number of coins picked.

Let's consider the possible scenarios:

Scenario 1: Alice picked 70 coins If Alice picked exactly 70 coins, then the remaining 130 coins must be divided among Buratino and Vasilio. Since Buratino picked fewer coins than anyone else, he must have picked fewer than 70 coins. Therefore, Vasilio must have picked more than 60 coins. However, it is not possible to distribute the remaining 130 coins among Buratino and Vasilio in a way that satisfies the conditions. Therefore, this scenario is not possible.

Scenario 2: Alice picked more than 70 coins If Alice picked more than 70 coins, then Buratino must have picked fewer than 70 coins. Since the total number of coins is 180 (20 bushes * 9 coins per bush), the remaining coins must be distributed among Buratino and Vasilio. However, we cannot determine the exact number of coins picked by Vasilio without additional information.

Based on the given information, we cannot determine the exact number of coins picked by Vasilio.

Answer 3

Problem Analysis

In this problem, there are 20 bushes along a road in the country of "DuRakov." Each bush has 9 coins. Passersby are allowed to pick 22, 33, or 44 coins from each bush, but they must not pick an equal number of coins from neighboring bushes, as this would result in their arrest by the guards. Alice, Buratino, and Vasilio walked along the road and picked all the coins. Alice picked at least 70 coins, while Buratino picked fewer coins than anyone else. We need to determine how many coins Vasilio picked.

Solution

To solve this problem, we need to consider the constraints and the information given. Let's break down the steps:

1. Alice picked at least 70 coins. 2. Buratino picked fewer coins than anyone else. 3. Vasilio picked the remaining coins.

Since Alice picked at least 70 coins, we know that the minimum number of coins picked by Alice is 70. This means that the maximum number of coins picked by Buratino is 69, as Buratino picked fewer coins than anyone else.

To find out how many coins Vasilio picked, we need to subtract the total number of coins picked by Alice and Buratino from the total number of coins available.

The total number of coins available is calculated by multiplying the number of bushes (20) by the number of coins on each bush (9), which gives us 180 coins.

Let's calculate the number of coins picked by Vasilio:

Total number of coins picked by Alice and Buratino = 70 + 69 = 139

Number of coins picked by Vasilio = Total number of coins available - Total number of coins picked by Alice and Buratino

Number of coins picked by Vasilio = 180 - 139 = 41

Therefore, Vasilio picked 41 coins.

Answer: Vasilio picked 41 coins.