一些逻辑训练的谜题：娜塔莎、十二点钟和茶
我的同事，娜塔莎喜欢小孩子，就给他们出了一些题。而我在十二点钟和娜塔莎闲谈时，总会为她补充一些，而她也觉得这还不错。到了下午，我们一起喝茶时，我们会把饼干放在鸟笼边，猫头鹰则会将其啄成碎片。我们的生活就是这样悠闲地度过的，和这所大学里的本科生的终日忙碌仿佛处在两个世界，他们没有心情欣赏校园里的建筑多么有艺术感，也看不见柳树和池塘蕴含着十四行诗——就算你不是莎士比亚也可以发现——只等着被抓出来和记录下来，但我们是刚好反过来的。
在这里，我会归纳一些我们设计的，助益于逻辑能力的谜题。
在这里，我会归纳一些我们设计的，助益于逻辑能力的谜题。
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I would love some help with this:
Let it be defined that an inconsistent trinity is a triangle where one of the three corners wear a different sign than the other two.
Let it also be defined that a consistent trinity is a triangle where all the three corners wear the same sign.
As shown:
Triangles such as ABC, ABD, ABE, etc. are inconsistent trinities. Triangles such as ACD and BEF are consistent trinities.
The problem is to prove or falsify the following statements:
1. It is impossible to make all triangles into inconsistent trinities no matter how we distribute the signs.
2. As we connect, mark, and sign all the dots (created by crossed lines), we can create infinitely more crossing points and triangles inside the hexagon. At any given moment, with the best effort<*>, there are potentially more inconsistent trinities than consistent trinities. True or false?
<*> "the best effort" means to create as many inconsistent trinities as possible.
Is it possible to show? Q2 is truly blowing my mind. Thanks in advance!
Let it be defined that an inconsistent trinity is a triangle where one of the three corners wear a different sign than the other two.
Let it also be defined that a consistent trinity is a triangle where all the three corners wear the same sign.
As shown:
Triangles such as ABC, ABD, ABE, etc. are inconsistent trinities. Triangles such as ACD and BEF are consistent trinities.
The problem is to prove or falsify the following statements:
1. It is impossible to make all triangles into inconsistent trinities no matter how we distribute the signs.
2. As we connect, mark, and sign all the dots (created by crossed lines), we can create infinitely more crossing points and triangles inside the hexagon. At any given moment, with the best effort<*>, there are potentially more inconsistent trinities than consistent trinities. True or false?
<*> "the best effort" means to create as many inconsistent trinities as possible.
Is it possible to show? Q2 is truly blowing my mind. Thanks in advance!
