Albert and Bernard just became friends with Cheryl,
and they want to know when her birthday is.  Cheryl gives them a list of
10 possible dates.

May 15	May 16	May 19
June 17	June 18
July 14	July 16
August 14	August 15	August 17

Cheryl then tells Albert and Bernard seperately the month and day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

(note: copied by me directly from the picture)

If you don't want spoilers you'd better stop reading and figure it out now.

What is truth? Is truth unchanging law? We both have truths.  Are mine the same as yours?- 39 Lashes

Let's start with one truth.  This is not a simple 5th grade math problem.

You see the meme is that this is a regular old word problem from a
5th grade math test that Singapore children are expected to pass in
order to graduate to the 6th grade which led of course to much Internet
hand wringing about the abysmal state of U.S. education in general and
particularly in STEM (Science, Technology, Engineering and Math) where
the privatizing looters of our School funds and fiscal conservatives in
general bemoan the lack of a qualified work force that must be
supplemented by smarter (and cheaper) H-1B imported slave labor.

Here's some tangential truth to start off- there is no shortage
of STEM qualified native labor, in fact there is a surplus.  The problem
is that they expect salaries commensurate with their expensive multi
year training.

Irrespective of that, almost every element of the meme is untrue.

This question is actually one of the more difficult math nerd questions given to high school students at a Math Olympiad.

Then there is some dispute about the semantics of the question.  The New York Times goes so far as to re-write it so it is undisputably true that
"seperately" in this case means that Albert knows only the month and
Bernard only the day instead of another fair interpretation of the word
that would mean merely that Cheryl told them independently.  I'll point
out the official language of Singapore is not just English, but British English (hell, they even drive on the wrong side of the road) so that's
kind of a minor, if glaring, quibble; the sort that ought to make Alex
Trebeck blush if not adjust the score during the commercial break (I
give it a 25% chance, but what the heck).

There is however a deeper, logical flaw that allows for two (count 'em, 2) "correct" answers that is explained by The Guardian's James Grime.

The 3 Easy Steps

1. Albert knows that Bernard doesn't know.

2. Albert deduces Bernard can't have a unique date such as 18 or 19.

3. Albert, smugly taunts Bernard, announcing Bernard doesn't know.

As we've seen above in The New York Times discussion, step one is dependent on what the definition of "is" is.
 Clearly if knowing the date (as Bernard does) provides a unique
solution, Bernard knows all which he admits he does not.  This
eliminates the 18th and 19th (you know my methods Watson).

The Difficult 4th Step

4. Bernard realises what Albert has realised,
which is that Bernard does not have 18 or 19. Now if Albert was holding
June he would know the answer, because there is only one remaining date
in June, namely June 17. So Bernard deduces it is not June.

The "Wrong" Answer- QED

5. Bernard announces he knows the answer. This is the second statement of the problem.

6. If Bernard is so confident, he must have a unique date. We know
it's not 18 or 19. What other unique date can it be? There are two 14s,
two 15s, two 16s and two 17s - but Bernard has eliminated June 17 -
leaving him with August 17 only. That's how he worked it out.

7. Albert is furious Bernard beat him to the answer. Albert puts
himself in Bernard's shoes, running through the six steps above. Finally
Albert reaches the same conclusion we have, Bernard must have 17.
Albert announces he knows the answer too.

So August 17 is a valid answer.

Or is it?

It is all about how you interpret the first statement. If Albert has to deduce that Bernard doesn't know, then we get July 16.

But if Albert knows that Bernard doesn't know - in other words, that
this is a statement of fact, rather than a deduction - then we get
August 17.

This incredibly subtle change - deduction vs fact - completely
changes the nature of the question. Indeed, with fact interpretation the
reader can now deduce the answer from just the first two statements of
the conversation, whereas the argument for July 16 does require all
three statements.

So, can we accept August 17?

Not any more. The originators of the question, Singapore and Asian School Math Olympiads, have rejected this alternative answer.

I'll point out that in most classic logical problems all the
statements are to be taken as fact rather than bluffs.  On the other
hand usually (but not always) all the information is relevant.

In any event I'm taking Alex to the mat on this one.  Jeopardy is an incredibly lucrative franchise and they give away only a pittance
in prizes.  I know plenty of lawyers (looking at you PhilJD) and I
think I get at least a settlement and an invite back.

The law that entropy always increases holds, I think,
the supreme position among the laws of Nature. If someone points out to
you that your pet theory of the universe is in disagreement with
Maxwell's equations - then so much the worse for Maxwell's equations. If
it is found to be contradicted by observation - well, these
experimentalists do bungle things sometimes. But if your theory is found
to be against the second law of thermodynamics I can give you no hope;
there is nothing for it but to collapse in deepest humiliation.

-Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)

Science and Technology News and Blogs

• Pluto's First Color Portrait From the New Horizons Probe, by Neel V. Patel, Wired
• Target Pluto: fastest spaceship set for epic encounter with our remotest planet, by Robin McKie, The Guardian
• Weird Bright Spots on Dwarf Planet Ceres Still a Mystery in New Maps by Elizabeth Howell, Space.com
• Rise and shine: Rosetta's Philae probe could be awake within weeks, by Hannah Devlin, The Guardian
• Here's mud in your eye: Rosetta's 'star trackers' muddled by comet dust, by Hannah Devlin, The Guardian
• Violent methane storms on Titan may solve dune direction mystery, by Peter Kelley, University of Washington Today
• Nasa's Curiosity rover finds water below surface of Mars, by Hannah Devlin, The Guardian
• Scientists hope Venus will give up the secret of how life evolved on Earth, by Robin McKie, The Guardian
• SpaceX Comes Close to Recovering Rocket, By KENNETH CHANG, The New York Times
• The Pacific Ocean has been slowing global warming down. That could be about to change, by Chris Mooney, Washington Post
• Mighty Rio Grande Now a Trickle Under Siege, By MICHAEL WINES, The New York Times
• In California, a Wet Era May Be Ending, By HENRY FOUNTAIN, The New York Times
• For Drinking Water in Drought, California Looks Warily to Sea, By JUSTIN GILLIS, The New York Times
• Four-year-old discovers 100-million-year-old dinosaur, By Joseph Dussault, The Christian Science Monitor
• Julius Caesar may have suffered mini-strokes, say doctors, by Ian Sample, The Guardian
• Cracked it! Scientists solve puzzle of why knuckles pop when pulled, by Ian Sample, The Guardian

Science Oriented Video

Obligatories, News and Blogs below.

The Breakfast Club (Lovin' Eyes Can Never See)

Welcome to The Breakfast Club! We're a disorganized group of rebel lefties who hang out and chat if and when we're not too hungover  we've been bailed out we're not too exhausted from last night's (CENSORED) the caffeine kicks in. Join us every weekday morning at 9am (ET) and
weekend morning at 10:30am (ET) to talk about current news and our
boring lives and to make fun of LaEscapee! If we are ever running late,
it's PhilJD's fault.

   

This Day in History

The Titanic sinks off the coast of Newfoundland;
President Abraham Lincoln dies; Jackie Robinson becomes first African
American player in MLB; US launches air raid against Libya; Pol Pot
dies; Joey Ramone dies.

Breakfast Tunes

Percy Sledge 1940 - 2015

Something to Think about over Coffee Prozac

In the end, it's not the years in your life that count. It's the life in your years.

Abraham Lincoln

Topic: 

• VOTS Community

Column: 

• The Breakfast Club

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