Final answer:
To make numbers 1 through 20 using six eights, one must creatively apply mathematical operations and concepts such as exponents and reciprocals. The task involves puzzles and experimenting with different methods to find multiple solutions.
Step-by-step explanation:
The student asked how to make the numbers 1 through 20 using six eights (e.g., 888÷888=1). This is a mathematics puzzle that involves using operations like addition, subtraction, multiplication, division, as well as parentheses and sometimes the factorial or power functions to arrange six instances of the digit '8' to form the numbers from 1 to 20.
It's important to use mathematical reasoning and understanding of concepts like exponents, reciprocal numbers, and division to tackle such problems. For instance, to find one eighth of 1,000, instead of division, you can multiply 1,000 by its reciprocal (which is 0.125) to get 125.
When dealing with multiplication and division of exponents, such as 10⁶ 10³, you can add or subtract exponents as appropriate. By experimenting with these operations and using quick experimentation, a student can find many paths to the answer, reinforcing the understanding that in math, there can be multiple solutions that lead to the same result.