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  • $\begingroup$ If A saw 4, wouldn't he only know that his number must be 3 or 4? How does he for sure know it's 4. $\endgroup$ Commented Feb 19, 2016 at 17:58
  • $\begingroup$ If his number was 3 (or any prime), B would necessarily know that his own was 4 (or $A+1$) since the only option for the two positive integers added or multiplied are $A$ and $1$. $\endgroup$ Commented Feb 19, 2016 at 18:00
  • $\begingroup$ Hmm. I think I got distracted in the midst of writing my answer. I will edit it. Thank you. $\endgroup$ Commented Feb 19, 2016 at 18:00