Numbers on heads

This is a stunningly good puzzle that just sounds totally impossible when you first hear it…

Three people are in a room each with a number on their forehead. They can see the other two people’s numbers but not their own. They all know that the numbers are positive integers and one is the sum of the other two. Each is trying to find their number, and the conversation goes like this:

Person A: “I don’t know my number”
Person B: “I don’t know my number”
Person C: “I don’t know my number”
Person A: “My number is 65”

Amazingly Person A is correct and worked this out purely by use of logic given what they all know and the conversation. No tricks at all!!

How is this possible? Have a try to figure it out before looking at the solution which you can find HERE