So, about this viral maths birthday problem …

Here’s a warm up joke:

Three logicians walk into a bar. The bar tender asks “Do all of you want a drink?”

The first logician says, “I don’t know.”

The second logician says, “I don’t know.”

The third logician says, “Yes!”

The following question went viral on Facebook. It had a sensationalising title: “Primary 5 [11 year old] mathematics question”, which later turned out to be incorrect as it was actually a Secondary 3 [15 year old] maths olympiad question.

I didn’t give much though to this question when I first saw it because I have seen such questions before so it wasn’t something new. But someone shared this with me in a private chat and so I thought might as well write a short blog post about how I solved it.

math1e

Solution:

We proceed by elimination since there are only 10 choices. A knows the month and B knows the day. Since A knows that B doesn’t know, we can eliminate options with a singleton-day date (an option where the day is unique), namely options with months May and June.

Reason: Proof by contradiction: Assume it is either May or June, then there exist a singleton-day date such that if B was given that day, then B would have known the date. But we know that A knows that B doesn’t know the date. Contradiction. So it cannot be May or June.

Which leaves us with

July 14, July 16
Aug 14, Aug 15, Aug 17

Second statement says B didn’t know at first (which is useless to us) but now B knows. It means that we can eliminate options that have the same day, namely July 14 and Aug 14. Otherwise B couldn’t have known.

Which leaves us with

July 16
Aug 15, Aug 17

The last statement says A now also knows the date. Which means the month must have only one option, similar reasoning in the previous paragraph. So the answer is July 16.

I came across this comment which included some Singlish translation of the problem which tickled me. The comment is included below. Enjoy!

mathse1comment

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