Question

Вдоль дороги в стране Дураков растут 40 кустов, на каждом кусте по 9 монет. Прохожие должны срывать с каждого куста 2, 3 или 4 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 140 монет, а Буратино сорвал меньше всех. Сколько монет сорвал Василио?

Answer 1

120 монет сорвал Василио. Так как Буратино сорвал меньше всех, значит срывал по 2, 3 монеты с каждого куста. 20 кустов умножаем на 2 монеты и 20 кустов на 3 монеты. Получаем, 100 монет сорвал Буратино. Складываем, то что сорвала Алиса и Буратино и получаем 240 монет. Умножаем 40 кустов на 9 монет и получаем 360 монет. От 360 монет отнимаем 240 и получаем, что Василио сорвал 120 монет.

Answer 2

Problem Analysis

In this problem, there are 40 bushes along a road in the country of "Durokov." Each bush has 9 coins on it. Passersby are allowed to pick 2, 3, or 4 coins from each bush, but they must not pick the same 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 140 coins, while Buratino picked fewer coins than anyone else. We need to determine how many coins Vasilio picked.

Solution

To solve this problem, we can use a simple mathematical approach. Let's assume that Alice picked a total of A coins, Buratino picked a total of B coins, and Vasilio picked a total of V coins.

Given that Alice picked at least 140 coins, we have the inequality:

A ≥ 140 Since Buratino picked fewer coins than anyone else, we have the inequality:

B < A We also know that there are 40 bushes, and each bush has 9 coins. Therefore, the total number of coins on all the bushes is:

Total coins = 40 * 9 = 360

Since Alice, Buratino, and Vasilio picked all the coins, we have the equation:

A + B + V = Total coins Now, let's solve these equations to find the value of Vasilio's coins.

Solution Steps

1. Start by assuming Alice picked the minimum number of coins possible, which is 140. 2. Calculate the maximum number of coins Buratino could have picked based on the inequality B < A. 3. Calculate the remaining coins that Vasilio must have picked based on the equation A + B + V = Total coins.

Let's calculate the values step by step.

1. Assume Alice picked 140 coins. 2. Buratino picked fewer coins than Alice, so let's assume Buratino picked 139 coins. 3. Calculate the remaining coins for Vasilio:

A + B + V = Total coins

140 + 139 + V = 360

V = 360 - 140 - 139

V = 81

Therefore, Vasilio picked 81 coins.

Answer

Vasilio picked a total of 81 coins.

References

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