You are in a group of six people. As you start to count the number of possible relationships between the different people in the group, you realize the maximum number is .

fifteen

Explanation:

To answer that, let's list the people:

Person number 1 Person number 2 person number 3 person number 4 person number 5 person number 6

Now let's organize them in a relationship order in which each one relates to different people:

Person number 1, can relate to person number 2, person number 3, person number 4, person number 5 and person number 6. Totaling 5 relationships.Person number 2 can relate to person number 3, person number 4, person number 5 and person number 6. Totaling a total of 4 relationships. Person number 3 can relate to person number 4, person number 5 and person number 6. Totaling 3 relationships. Person number 4 can relate to person number 5 and people number 6. Totaling 2 relationships. Person number 5 and 6 can only relate to one another. Totaling 1 relationship.

Now if we add up the relationship totals for each person (5 + 4 + 3 + 2 + 1), we will realize that it is only possible to have 15 relationships between different people within a group of 6 people.