**Question**

**Introduction**

This “Primary
5 mathematics” (actually an upper secondary Olympiad) logic puzzle has gone viral. It has been making its rounds in various
forums in Singapore
and overseas, stumping adults and children alike. It is actually a parody of an old puzzle. Can it even be solved? It seems that there is no information given by
each parties that we can exploit. Actually
there is! In a subtle way ...

**Solution**

In the
beginning, everybody knows that Albert knows only the month and Bernard knows
only the numerical day of the month.

When Albert
tells us “I don’t know when Cheryl’s birthday is, but I know that Bernard does
not know too.” he is leaking out information (from his knowledge of the month) that
the day of the month appears more than once and cannot be (June 18 or May 19). Actually, the original phrasing is more like “

**If**I don’t know when Cheryl’s birthday is,**then**Bernard does not know too.”. The person who set this question merely changed the names of the people and the dates, without appreciating the subtle but crucial difference between a statement of**and an***fact***(an “if ... then ... ” statement).***implication*
Ruling out June
18 and May 19, we also know that Albert knows that the birthday month is
neither June nor May. Otherwise, how
would he have been so confident in saying that he knows Bernard would not know Cheryl’s
exact birthday? So we can eliminate
those months.

Bernard
acknowledges the above state of affairs and the embedded hint. With the choice narrowed down and with his
knowledge of the numerical date, he now knows Cheryl’s birthday. Since we know that Bernard knows Cheryl’s
birthday, we know that it cannot be a numerical date that appears more than
once (otherwise he would not have been able to know). So we can cross out July 14 and August 14.

Now Albert would
telepathically thank Bernard for this helpful hint. Because now he is able to deduce Cheryl’s
birthday with his knowledge of the month. That would mean that this cannot be a month
with two candidate dates. We blot out
the August dates and see for ourselves the only remaining possibility.

**Conclusion:**Cheryl’s birthday is July 16.

**Remarks**

This puzzle was solved using the process of
elimination and analysing our knowledge of what each party knows and can
know. Thus we successively narrow down
the possibilities until the answer becomes obvious. Here we learn that

knowledge of other people’s
knowledge can itself give us knowledge.

This principle is actually employed in Sensitive information in certain organisations
is restricted on a “

*(the use of secret codes) which finds applications in fields like***cryptology***banking*, the*military*(cf. interesting story of how the German Enigma code was broken in WorldWar II) and*communications*. As an example, radio communication can tell the enemy of troop positions and warn of an impending attack, and that is why*radio silence*is imployed as a precaution.*need to know*” basis.**Suitable Levels**

*****Upper Secondary Olympiad

* other syllabuses that involve knowledge or epistemology

* application of mathematical principles in real life

* for all people interested in logic puzzles

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