I received this question from a friend yesterday and was really amazed at the type of question that primary 5 students nowadays have to answer. After a long time, I managed to figure out the answer, that is of course after going through a few tries. But somehow the explanation doesn’t sound logical to me. Or am I just too slow to understand? So here is the question:

I have come across a similar question somewhere two years back on Facebook, but till today, I have difficulty understand it. Maybe any kind souls out there would like to share your answer and explanation?

Updated Post

So after a day of researching, talking to people and taking some time to understand, I finally manage to get the answer to this question, July 16. However, knowing the answer won’t be enough without understanding it right? There are many ways to explain and the first that came out to me was this:

Reading through the solution, you find that the second statement and third statement make a lot of sense. But somehow I was stuck with understanding the first statement. I know that Bernard will remove 18 and 19, but I do not understand why all dates in May and June have to be remove as well. After more consultation from a friend, who once work as a teacher, this was his explanation in his own words:

So after the first statement, we actually have to look from both Albert’s and Bernard’s POV: Bernard knows the number, so 18 and 19 is definitely out if not he would have guessed the correct date. Then we have to look at Albert’s POV, he knows the month and he is 100% sure Bernard will not be able to guess it, precisely because the month he knows is not May and June, where there is still a probability that Bernard might have guessed the dates could be in May or June as 19 and 18 are appeared in these months respectively. I think this is the hardest part to understand and if I were to understand it easily, the key is “for 100% certainty Albert is sure Bernard doesn’t know”, so yeah 18, 19, May June all are out.

But don’t worry, finally someone posted on the internet the model answer to this question, said to be taken from Singapore and Asian Schools Math Olympiad:

  Pic taken from Mothership.sg

So finally, do you understand now?