GIVEN POSITIVE INTEGERS X AND Y , BOTH GREATER THAN 1, BU...

10. Given positive integers

x and y , both greater than 1, but not necessarily different.

The product xy is written on Albert’s hat, and the sum x

+

y

is written on Bill’s hat.

They can not see the numbers on their own hat. Then they take turns to make the

statement as follows:

Bill: “ I don’t know the number on my hat.”

Albert: “ I don’t know the number on my hat.”

Bill: “I don’t know the number on my hat.”

Albert: “Now, I know the number on my hat.”

Given both of them are smart guys and won’t lie, determine the numbers written on

their hats.

Answer: Albert’s number =__________, Bill’s number =____________.