You know that Singapore math problem that people have been struggling to solve? Here’s one easy way to figure out Cheryl’s birthday, step by step.
Let’s start with the original problem.
Cheryl has 10 possible dates for her birthday: May 15, 16, 19; June 17, 18; July 14, 16; and August 14, 15, 17.
Then we have Albert’s opening statement: “I don’t know when your birthday is, but I know Bernard doesn’t know, either.”
The second half of what Albert says is key here. Because Albert knows Bernard doesn’t know, that means Cheryl’s birthday can’t be May 19th or June 18th, because if Cheryl had whispered “18” or “19” in Bernard’s ear, he would have known her birthday, as there are no other possibilities for the 18th or 19th.
Based on Albert’s statement, we can also eliminate the other days in May and June. Why? Because if Albert KNOWS Bernard doesn’t know, Cheryl must have whispered either “July” or “August” in his ear.
If Cheryl had whispered “May” or “June” in Albert’s ear, he could not be 100% certain Bernard did NOT know, as Cheryl could have whispered “18” or “19” in Bernard’s ear.
So the first statement from the problem has now been parsed, and we are left with five possible birthdays: July 14th and 16th, and August 14, 15, and 17.
Now, we move to Bernard’s statement: “At first I [didn’t] know when Cheryl’s birthday is, but I know now.”
Assuming Bernard is not lying and he has figured out his remaining options from Albert’s statement (which is a prerequisite for any logic problem), we can eliminate both July 14th and August 14th. If Cheryl had whispered “14” to Bernard, he would not know at this point, but he does.
That leaves July 16th, August 15th, or August 17th.
And now Albert’s final statement: “Now I know too!”
If we apply the same test as before, that Albert is not lying and is clever enough to know the remaining options, we can use the same method as step 4, but with months instead of days.
If Cheryl had whispered “August” in Albert’s ear, he would not have said “I now know too!” because both August 15 and 17 are still on the table. He would have said something like “I still don’t know” or “I’ve got it down to two options, stop pressuring me!” or “Cheryl you’re the worst friend ever.”
Therefore, the answer must be July 16th.
If you made it through all of those steps without getting lost, congratulations, you’re as smart as Singaporean mathletes, whom we’re guessing are pretty dang smart.