Question

Одиннадцать шестиклассников встали в круг. Они договорились, что некоторые из них всегда говорят правду, а все другие всегда лгут. Каждому из них раздали по две карточки, и каждый сказал: "У меня карточки одного цвета". После этого каждый передал обе свои карточки своему соседу справа. Могли ли они все после этого сказать: "У меня теперь карточки разных цветов"?

Answer 1

Да они бы могли сказать разных цветов
ответ:они сказали у нас разные карточки

Answer 2

Problem Analysis

Eleven sixth-graders are standing in a circle. They have agreed that some of them always tell the truth, while all the others always lie. Each student is given two cards, and each student says, "I have cards of the same color." After that, each student passes both of their cards to their right neighbor. The question is whether they can all say, "I now have cards of different colors."

Solution

To solve this problem, let's analyze the situation step by step:

1. Each student initially has two cards of the same color. 2. Each student passes both of their cards to their right neighbor. 3. After the cards are passed, each student will have two new cards, one from their left neighbor and one from their right neighbor.

Let's consider the possible scenarios:

Scenario 1: All students initially have cards of the same color. In this scenario, when the cards are passed, each student will receive one card of the same color from their left neighbor and one card of the same color from their right neighbor. Therefore, they will still have cards of the same color, and they cannot all say, "I now have cards of different colors."

Scenario 2: At least one student initially has cards of different colors. In this scenario, when the cards are passed, each student will receive one card of the same color from their left neighbor and one card of a different color from their right neighbor. Therefore, they will have cards of different colors, and they can all say, "I now have cards of different colors."

Based on this analysis, if at least one student initially has cards of different colors, they can all say, "I now have cards of different colors." Otherwise, if all students initially have cards of the same color, they cannot all say, "I now have cards of different colors."

Conclusion

If at least one student initially has cards of different colors, they can all say, "I now have cards of different colors." Otherwise, if all students initially have cards of the same color, they cannot all say, "I now have cards of different colors."

Please let me know if anything is unclear or if you have any further questions!