10.6. Ramsey Numbers

Try these first

1. 1.

   What does a Ramsey number represent?

   Hint

   Think about friendship or enmity dynamics in groups.

2. 2.

   How many people must be present to ensure 3 mutual friends or enemies?

   Hint

   This is a specific outcome related to R(3, 3).

3. 3.

   What is the value of R(3, 3)?

   • 5
   • 6
   • 7

   Hint

   Recall our discussions around this specific number.

4. 4.

   True or False: There exists a generic formula to find any Ramsey number.

   • True
   • False

   Hint

   Think about the implications of group dynamics.

5. 5.

   Design a scenario with a specific group size and describe the potential friendships and enmities, while illustrating its relation to Ramsey numbers.

   Hint

   Use different configurations of friend/enemy arrangements.

6. 6.

   Explain a real-world situation where Ramsey theory might apply and the implications of friendship dynamics.

   Hint

   Consider how friendships and enmities operate on social media platforms.