You have a friendship club. There are 12 members in your club. On the twelfth day of each month, you have a friendship call. Each member of the club talks to every other member that day by phone. This way everybody expresses his or her friendship with each other. How many conversations are made on that day?

There are a total of 66 conversations.

Step-by-step explanation:

Ok, we have 12 members.

let's call them:

member 1, member 2, member 3, etc...

Let's assume that member 1 starts talking to the others, then he talks to:

member 2, member 3, member 4, etc.

So member 1 talks to the other 11 members.

We have already 11 conversations.

Now let's count the conversations of member 2.

He talks to member 1, member 3, etc.

But the conversation between member 1 and member 2 was already counted, so we do not count it this time, then here we have other 10 conversations.

now for member 3. He talks with member 1, member 2, member 4, member 5, etc...

But conversations between member 1 and member 3, and member 2 and member 3 are already counted, so here we have 9 new conversations.

We already can see the pattern here.

For each new member that we count, the number of conversations is one less than for the previous member.

The total number of conversations will be:

11 + 10 + 9 + 8+ 7 + 6+5 + 4 + 3+ 2+ 1 = 66