Let's assume that this bag of sugar has x pieces. According to the description of the topic, we can get the following two equations: x=4n+ r(n is an integer and r is a remainder), x.

Since x must be divisible by 12, we can rewrite the first equation as x-4n= r, and then substitute this equation into the second equation to get x-4n < 5m. This means x.

We need to find the smallest positive integer x that satisfies the above conditions. Through observation and experiment, it can be found that when n= 1, r = 3；; When n=2, r = 8；; When n=3, r =13; And so on. So the smallest x should be 4× 1+3=7. But 7 is not divisible by 12, so we need to keep trying.

When n=4, r =18; When n=5, r = 23, when n=6, r = 28 and so on. We find that when n=6, r=28 is an appropriate solution. X=4×6+28=40. 40 is divisible by 12, and 40-4×6=28, which meets the requirements of the topic (four yuan per person and eight yuan per person). So, this bag of sugar has at least 40 pieces.

Benefits of learning mathematical numbers:

1 can be applied to various fields, including science, technology, engineering and mathematics itself. By studying mathematics, you can learn how to analyze problems, draw conclusions and verify whether these conclusions are correct.

2. Improve the ability to solve problems: Mathematics provides many skills and methods to solve problems. Learning mathematics can help you better understand and solve various problems, including some practical problems and abstract problems. In addition, mathematics can help you better understand other subjects, including physics, chemistry, computer science and so on.

3. Enhance memory: Learning mathematics requires memorizing many formulas and theorems. Remembering these formulas and theorems can help you better understand mathematical concepts and problem-solving methods. In addition, by constantly practicing and applying these formulas and theorems, we can enhance our memory and improve our learning ability.