Question 11
Players $A$ and $B$ wrote down two positive integers each on a black board. The product of the two numbers $A$ wrote is twice the sum of the two numbers $B$ wrote, and the product of the two numbers $B$ wrote is twice the sum of the two numbers $A$ wrote, and furthermore, the sum of the two numbers $A$ wrote is greater than or equal to the sum of the two numbers $B$ wrote. Determine all possible values for the sum of the two numbers $B$ wrote. Note that four numbers written down need not be distinct.