A, B and C are three persons among a set P of n (n[u]>[/u]3) persons. It is known that A, B and C are friends of one another, and that every one of the three persons has already made friends with more than half the total number of people in P. Given that every three persons who are friends of one another form a [i]friendly group[/i], what is the minimum number of friendly groups that may exist in P?
To find the minimum number of friendly groups that may exist in \( P \), we need to analyze the given conditions and apply combinatorial principles.

### Case 1: \( n = 2k \)
1. **Determine the number of friends each person has:**
   Each of \( A, B, \) and \( C \) has more than half the total number of people in \( P \) as friends. Since \( n = 2k \), each person has more than \( k \) friends. Excluding \( A, B, \) and \( C \) themselves, each of them has more than \( k-2 \) friends among the remaining \( 2k-3 \) people.

2. **Apply the Pigeonhole Principle:**
   By the Pigeonhole Principle, there must be at least \( k-3 \) persons who are friends with at least two of \( A, B, \) and \( C \). This is because each of \( A, B, \) and \( C \) has more than \( k-2 \) friends, and there are \( 2k-3 \) other people.

3. **Count the minimum number of friendly groups:**
   The minimum number of friendly groups is reached if \( A \) and \( B \) have \( k-3 \) common friends and 1 distinct friend each. This leaves \( k-2 \) friends for \( C \). Therefore, the minimum number of friendly groups is \( k-2 \) (including the group \((A, B, C)\)).

### Case 2: \( n = 2k+1 \)
1. **Determine the number of friends each person has:**
   Each of \( A, B, \) and \( C \) has more than half the total number of people in \( P \) as friends. Since \( n = 2k+1 \), each person has more than \( k \) friends. Excluding \( A, B, \) and \( C \) themselves, each of them has more than \( k-2 \) friends among the remaining \( 2k-2 \) people.

2. **Apply the Pigeonhole Principle:**
   By the Pigeonhole Principle, there must be at least \( k-2 \) persons who are friends with at least two of \( A, B, \) and \( C \). This is because each of \( A, B, \) and \( C \) has more than \( k-2 \) friends, and there are \( 2k-2 \) other people.

3. **Count the minimum number of friendly groups:**
   The minimum number of friendly groups is reached if \( A \) and \( B \) have \( k-2 \) common friends and 1 distinct friend each. This leaves \( k-1 \) friends for \( C \). Therefore, the minimum number of friendly groups is \( k \) (including the group \((A, B, C)\)).

The final answer is \( \boxed{ k-2 } \) for \( n = 2k \) and \( k \) for \( n = 2k+1 \).