Stephanie is a new student in the new school, but she is cheerful and natural. Mrs. Gucci left homework for the children, that is, to find the sum of 1 to 100. Stephanie blurted out "5050". Justin and I are both curious about how Stephanie calculated the result accurately in such a short time. The original numbers were grouped in pairs, 1+99, 2+98, 3+97 ... until 49+5 1, and 49 logarithms were used, each logarithms was 100, so 44. These two numbers add up to get 5050. By matching, you can also calculate the number of 1+ ...+1000,1+...+10000. Children are very interested in mathematics and set up a math club called "Math Little Genius Detective Team". The first problem that children have to solve is the problem of seat arrangement. "Try to get eight people to sit around the round table: Amy and Linda must sit next to each other, Brad and Beth must sit next to each other, Charles must sit next to Debbie or Emily, Francis and Debbie must sit next to each other, Amy and Linda cannot sit next to Brad and Beth, Charles cannot sit next to Brad, Francis cannot sit next to Brad, Debbie and Emily cannot sit next to each other, and Amy cannot sit next to Charles." Draw a round table and number the seats. Sometimes a math problem has more than one answer.

The series of "Mathematical Genius Detective Team" tells that Jordan, Justin and Stephanie are all mathematical wizards in the school. In order to solve more mathematical problems and give full play to the role of mathematics in life, the three of them set up an extracurricular mathematics club-the mathematical genius investigation team.