If you want to enliven the atmosphere, I can give you a lot of topics suitable for senior one's mathematical thinking, but if you cooperate with what you have learned, I can give you two topics for reference.

Eight steel balls look the same (exactly the same shape), and one of them is overweight. Now I have a balance. How can you choose this overweight steel ball (selected from Microsoft recruitment questions) only after weighing it twice?

//Kao's thought is: classification thought.

There is another topic:

There is a glass of water in the cup, which is full. Every time I take a sip of water, I drink half of the water in the cup. We know that it is inexhaustible, and there is always water in the cup.

(fallacy in mathematics) A little dog ran to its master. We imagine that if the puppy wants to run to its owner, it must run half the way to them first. When it runs halfway to its owner, the puppy must continue to run halfway to their owner. When the puppy runs to its owner, it must run half the distance to achieve its goal ... We know that the puppy can run to its owner's side, and may even run forward beyond its owner.

The problem is that we regard the bottom of a glass of water as a reference point. Similarly, we regard the owner as a reference point, so that the dog and the water in the cup can be regarded as moving towards them. Why are there different results?

What is the root cause of the problem that is easy to understand? I thought of this question the other day. If there is no answer, please leave me a message.