Question

Чебурашка и крокодил Гена воюют против 2017-голового змея Горыныча. Чебурашка рвётся в бой первым. Они подходят к нему по очереди и отрубают либо 2, либо 3 головы. Сможет ли он победить (то есть отрубить последнюю голову)?

Answer 1

Нет. он не будет последним кто отрубит голову змею

Answer 2

Нет не сможет, это сделает крокодил

Answer 3

Answer in detail. Cheburashka and Crocodile Gena are fighting against the 2017-headed snake Gorynych. Cheburashka rushes into battle first. They approach him one by one and cut off either 2 or 3 heads. Can he win (that is, cut off the last head)?

This is a very interesting question. I will try to answer it using some logic and mathematics.

First, let us assume that Cheburashka and Crocodile Gena can cut off any number of heads from 1 to 3, as long as they do not exceed the total number of heads left. For example, if there are 5 heads left, they can cut off 1, 2, 3, 4, or 5 heads.

Second, let us define a winning position as a situation where the number of heads left is divisible by 4. For example, if there are 8, 12, 16, or 20 heads left, then it is a winning position. This is because, no matter how many heads the snake cuts off, the remaining number will not be divisible by 4, and the next player can always cut off enough heads to make it divisible by 4 again. For example, if there are 12 heads left, and the snake cuts off 3 heads, then there are 9 heads left, and the next player can cut off 1 head to make it 8, which is a winning position.

Third, let us analyze the initial position, where there are 2017 heads. This is not a winning position, because 2017 is not divisible by 4. Therefore, the snake has an advantage, and can always force a loss for Cheburashka and Crocodile Gena, if it plays optimally. For example, if Cheburashka cuts off 2 heads, then there are 2015 heads left, and the snake can cut off 3 heads to make it 2012, which is a winning position. If Cheburashka cuts off 3 heads, then there are 2014 heads left, and the snake can cut off 2 heads to make it 2012, which is also a winning position.

Therefore, the answer is no, Cheburashka and Crocodile Gena cannot win, unless the snake makes a mistake and cuts off a number of heads that leaves a winning position for them. However, this is very unlikely, because the snake has 2017 heads, and probably knows how to count.

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