Party at Dr. Hong's House

During the COVID-19 lock down, CMM was conducted online. Many students don't know each other before. After the lock down, Dr. Hong invites a few CMM students to his house for a party. To make sure that the students can have fun with each other, Dr. Hong invites as many students as he can under the condition that among each three students, there are two who know each other and two who don't know each other. How many students were invited by Dr. Hong?

Biggest V

In the following expression, ONE + TWO + FOUR = SEVEN, different letters represent different nonnegative integers. What's the largest possible value for V?

Greatest Common Factor

What's the greatest common factor of 25200, 14850 and 8190?

Sum of Digits

What's the sum of digits of 999,999,999 × 666,666?