
Cheryl's Birthday: Singapore's maths puzzle baffles world - cjr
http://www.bbc.co.uk/news/world-asia-32297367
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kjak
See also

[https://news.ycombinator.com/item?id=9375643](https://news.ycombinator.com/item?id=9375643)

[https://news.ycombinator.com/item?id=9367438](https://news.ycombinator.com/item?id=9367438)

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pango
My logic for this puzzle goes as follows:

1) Albert knows Bernard cannot know the answer immediately. As 18 and 19 are
days that only appear once, the month must not contain those dates, so May and
June are eliminated.

2)Bernard is able to identify the month based on knowing it can't be june or
may and based on his date. Therefore Bernard cannot have had the number 14. He
must have 15,16, or 17.

3) Knowing it is 15, 16, or 17 uniquely identifies the date for albert. Since
august has 2 options left, it must be july, and the only date available is
July 16.

This is a tricky problem, but it is one that is fairly straightforward to
approach step by step. Definitely appropriate for advanced students at age 15.
The problem reminds me of the question about how many people on an island have
blue/brown eyes.

I haven't done logic problems in a long time, so I may have erred and would
welcome alternative interpretations.

~~~
whoopdedo
[https://www.xkcd.com/blue_eyes.html](https://www.xkcd.com/blue_eyes.html)

The island puzzle, for those who haven't seen it yet.

I think that one is much more difficult because the problem is stated in a way
that makes the readers think she has much less information that is actually
given. The birthday problem has no trick phrasing in it.

Well, maybe a little tricky. You'd get stuck if you tried to reason from four
months and six days. This would be a likely mistake if the problem were read
aloud with the list of dates as "May 15, 16, and 19, or June 17 and 18..."

Recognizing that Albert and Bernard are both working with sets of 10 elements
each -- one for each possible date -- then it becomes a simple graph problem.

Write a chart with rows labeled months and columns labeled days. Put a mark on
each possible date. Albert circles one row and Bernard one column. Albert says
none of the marks in his rows are the only marks in their columns, so draw a
line through the columns with only one mark and the rows that intersect at
that mark. Bernard says there is only one mark in his column after eliminating
the row, so draw a line through the columns with more than one mark. Albert
says there is only one mark in his row, so draw a line through the row that
still has two marks in it. The only one left is July 15.

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lotsofmangos
July 16th

can't be any of the months with unique numbers, so May and June are out

It can't be 14th therefore as you are still confused between July and August

If it was 15 or 17, then there would still be confusion about which, so Albert
must have been told July and Bernard must have been told 16

edit - BBC baffles world by claiming basic logic puzzles baffle world.

edit 2 - This attitude to maths in news reports is utterly poisonous. The
papers publish more difficult sudokus daily in their puzzle section.

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codeonfire
I think there are two solutions. The video in the link gives one, the other is
June 17. Supposing Albert knows the day, his statement eliminates June 18 and
May 19. Bernard claims to know the answer, which can only be June 17. Albert
does the same logic and reaches the same conclusion.

~~~
sago
Your second solution depends on interpreting the "Albert knows Bernard doesn't
know" to mean that Bernard _told_ (or otherwise signalled to) Albert that he
doesn't know, rather than Albert deducing that Bernard couldn't know.

There was a detailed rebuttal of this interpretation by the folks who set the
original question.

But it is easy to claim "that's not what I meant!" Actually being precise
about what you mean is fiendishly difficult. I recommend Imre Lakatosh's
excellent book on proofs "Proofs and Refutations" \- its short, and thoroughly
dismantles the early 20th century ideas that math is somehow a precise
conceptual structure independent of language ambiguities.

Or put another way: with enough eyeballs, all language is ambiguous.

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alienchow
1\. Albert has July, so he knows all the days Bernard could have been given
have duplicates. Thus, he knows Bernard doesn't know the birthday yet.

2\. Bernard hears this and knows Albert is holding on to either July or
August. He holds a number that is unique within these 2 months. That is why he
now knows the birthday.

3\. Albert now knows that Bernard knows, and thus has a day that is unique
between July and August. Which means it cannot be 14.

4\. So among July 16, August 15, and August 17, the only way Albert can know
for sure is if he is holding on to July.

Therefore July 16.

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GnwbZHiU
They all have communication issue, or they use too much gadgets as they have
lost their social skill.

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sownkunz
apparently they need to focus more on English than math

