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

Заметим что 9=2+3+4 то есть с куста можно сорвать 2 3 и 4 монеты
Алиса щла первая и рвала сотответсвенно 4 3 4 3 ... 4 3 монеты, или 3 4 3 4 .... иначе ее бы арестовали . И набрала (4+3)*20=140 монет 
Значит осталось висеть на кустах после Алисы 6 5 6 5 6 5..... или 5 6 5 6  5 6...
5=2+3 6=2+4 других вариантов нет и 2 встречается два раза значит буратино должен рвать еще 3, чтобы набрать наименьшее количество то есть Буратино рвал 3 2 3 2 .... Итого (2+3)*20=100
Значит Базилио срывал 2 4 2 4 2 4 ... Итого (2+4)*20=120
Алиса 140 Базилио 120 Буратино 100   

Answer 2

Problem Analysis

In this problem, there are 40 bushes along a road in the country of "Дураков" (which translates to "Fools"). 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 doing so 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 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 need to find the number of coins picked by Vasilio. Let's break down the problem step by step:

1. Alice picked at least 140 coins. 2. Buratino picked fewer coins than anyone else. 3. Vasilio is the remaining person, so we need to find the number of coins he picked.

Let's assume that Alice picked exactly 140 coins. Since Alice picked the most coins, Buratino must have picked fewer than 140 coins. Therefore, Buratino could have picked any number of coins less than 140.

Now, let's calculate the number of coins picked by Vasilio. Since there are a total of 40 bushes and each bush has 9 coins, there are a total of 40 * 9 = 360 coins on all the bushes.

If Alice picked exactly 140 coins, and Buratino picked fewer than 140 coins, then the remaining coins must have been picked by Vasilio. Therefore, Vasilio picked 360 - 140 - (number of coins picked by Buratino) coins.

To find the number of coins picked by Vasilio, we need to subtract the number of coins picked by Buratino from the remaining coins. Since we don't know the exact number of coins picked by Buratino, we cannot determine the exact number of coins picked by Vasilio.

In conclusion, we cannot determine the exact number of coins picked by Vasilio without knowing the number of coins picked by Buratino.