>>12355012If Albert knows that Bernard can't know from the date alone, then it cannot be dates 18 or 19 which are unique.
From this Bernard gathers that it cannot be months May nor June. It must be in July or August.
Bernard then claims to know the date, which eliminates the date 14 since it is shared by July and August.
From Albert's perspective the remaining dates are July 16, August 15, and August 17. However, Albert claims to know the date thus he must have been told that it was the month of July.
Cheryl's birthday is July 16.