Problem Description
There are 1,000 identical bottles, 999 of which are ordinary water, and one bottle is toxic. The mouse that drank the poison will die within 24 hours. Ask how many mice are needed to find the poison in 24 hours. That bottle of water?
When I first saw this question, I was confused, and after a short thought, I thought it should be 999 white mice. After all, there is a time limit, but I also wonder if there are other better answers. After all, this answer It's too direct.
(Actually, 999 is not the correct answer! If you are seeing this question for the first time, you may wish to spend 1 minute thinking about your answer)
Problem-solving ideas
The correct answer is 10, and on this basis, the following questions can be extended: at least a few mice will die, each mouse will drink an average of several bottles of water, and when the last bottle of water is poisonous, which ones died White mice and so on. Faced with these seemingly complicated questions, how should you answer them?
After seeing 10 answers, my feeling was first of all surprised that I could detect the poisonous bottle from 1000 bottles of water with so few mice, which is far from the answer I thought of, if I really want to Using my own stupid method, how much resources have to be wasted ... Let's think about how to use 10 mice to find the only toxic bottle of water from 1000 bottles of water. After a few minutes of thinking, I still did not want to understand why there were 10. After the teacher's explanation, I understood the way of thinking about this question-computer thinking!
To encode 1000 bottles from 0 to 999, to convert to a binary representation requires a 10-bit binary number, 0000000000 ~ 1111100111, and then each of them corresponds to the corresponding number of the mouse, and 0 means that the mouse does not drink A bottle of water with a value of 1 means that the little mouse is drinking the bottle of water. After 24 hours, by observing the number and number of dead little mice, it can be inferred which specific number of water is poisonous. Only 10 mice are needed to get the result! Moreover, on the basis of this numbering system, the extended problems can be reversed.
understanding
It can be seen that the thinking of the above problem is actually to use the most essential function of the computer-codec technology, to solve the problem abstraction through coding, to convert a problem in the decimal world into a binary problem, by converting a linear Problems, increase the dimension, expand into a multi-dimensional problem expression, ascending dimensional thinking, and become a problem covered by the numerical range.
The above problem-solving ideas are abstracted into a mathematical modeling formula, which is actually the following formula:
N = log2x
is that with this simple formula, it can solve a seemingly extremely complicated problem. This is the charm of mathematics. Abstract from life and return to life problems.
summary
Learning content and methods
- After understanding this question, I re-learned the knowledge of codec and gained a deeper understanding of the application of codec
- The seemingly difficult problem, from another angle, another way of thinking, becomes extremely simple. Ascending dimensional thinking, dimensionality reduction and disassembly (refining the way of thinking about coding and decoding, decomposing a linear problem into ten-dimensional problems)
- Learning is a process of continuous summary and repetition. When you encounter a concept or a knowledge point, you need to move your thinking up and refine the summary. At the same time, you must also relate to the real case around us (transform the concept into an equivalent figure , Images, etc.).
Reflection
For my previous learning and knowledge, I feel that there is a certain distance from myself, and I can't deeply understand it. Recently, I finally found the crux: I can't convert the learned content into my own subjective understanding and contact with the specific things around me. Learning is actually a very subjective and highly personalized thing. How abstract the content learned can always be mapped to our existing knowledge system, so that there are practical cases associated with it, learning becomes easy and simple By the way, we will naturally learn well. I believe that our learning efficiency can be increased ten times and one hundred times!
