How to Answer This ‘Classic Logic Question’?
The said “classical logic question” for high schoolers is making rounds online. But I never encounter this logic question in my entire life.
According to Singaporean news site The Straits Times, the photo was posted by TV presenter Kenneth Kong on Facebook which garnered almost 5000 shares as of writing.
On his post, Kong said that the question causes debate between him and his wife.
What is more interesting in the problem, it was given to 5th grade students.
Some people say it was a classical logic problem. I am a math enthusiast, why in the world I haven’t encounter this classic logic problem my whole life?
Here is a neat solution presented by Tata Lino
Albert == Month
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
(Eliminating unique numbers 18 and 19… Thus May and June is eliminated)
Possible birthday is July and August
Bernard == Date
Bernard: At first I don’t know when Cheryl’s Birthday is, but I know now.
(so it’s not 14, Possible birthday is July 16, August 15 and August 17, but since Bernard has the date he knows Cheryl’s birthday!
Albert: Then I also know when Cheryl’s birthday is
(If Albert has August then he cannot say this statement, thus he have July as the month)
Thus July 16 is the birthday of Cheryl
Another solution from one of the International Mathematical Olympiad bronze medalists Kyle Patrick Dulay of Philippine Team.
If Cheryl’s birthday was in May or June, then Albert cannot make the first statement because Bernard could know Cheryl’s birthday if her birthday was May 19 or June 18.
Thus, her birthday is in July or August.
Bernard, knowing this, deduced Cheryl’s birthday. Therefore, the day cannot be 14 (if it was, he wouldn’t be able to know Cheryl’s birthday because it could be July 14 or August 14).
Finally, if Cheryl’s birthday was in August, then the information above is still insufficient for Albert to make a conclusion (her birthday could be August 15 or 17). Therefore, based on the last statement, her birthday must be in July.
Her birthday must be July 16.