
Xkcd strip used as a exam question - adambyrtek
http://i.imgur.com/fT0DA.png
======
Steuard
A friend of mine created a nicely organized database of xkcd strips to help
teachers find subject-appropriate examples:

<http://andromedayelton.com/dckx.php>

Some topics clearly show up more often than others...

------
tw1st3dst33l
This isn't really surprising.I usually find myself wishing that Randall Munroe
(author of XKCD) would teach most of my classes. Not only is he a polymath,
but he's completely insane. Those are the best teachers.

~~~
hugh3
I'm rather unconvinced that Randall Monroe is a polymath.

~~~
wahnfrieden
He postures himself as one, at least.

~~~
hugh3
I'd go so far as to say he's _interested_ in a lot of stuff, but his actual
level of knowledge is pretty much "dude with a Bachelor's Degree and access to
wikipedia".

Nothing wrong with that, but let's not get too excited.

~~~
Natsu
> "dude with a Bachelor's Degree and access to wikipedia"

Yeah, but that's actually pretty smart. There are a lot of people who haven't
yet figured out that you can look up almost _anything_ online....

------
jtdowney
We show Exploits of a Mom (<http://xkcd.com/327/>) with the moms last speech
bubble blanked out to candidates during interviews. You might be surprised how
many have trouble explaining what is going on.

~~~
kenjackson
I didn't get it until the last bubble. I thought the son did the exploit and
the mom was covering for him. I'm still unclear if that was actually the
childs name or this was a one-off exploit by the mom.

~~~
wahnfrieden
Does that really matter?

The parent poster is saying that interviewees don't get what's going on _with
the exploit itself_.

~~~
kenjackson
But they pretty much show the exploit in the previous pane... How could they
not get the exploit?

~~~
cmelbye
That's the point. If the candidate doesn't know that that is a SQL injection,
then you have a problem.

------
Maxious
I've seen this one used in an Introduction to Psychology exam:
<http://xkcd.com/32/> And the velociraptor problem was a class exercise for
calculus: <http://www.xkcd.com/135/>

------
jawee
The best I've had in my experience is a Calvin and Hobbes strip, but they're
probably too classic to matter.

<http://www.gocomics.com/calvinandhobbes/1995/08/23> I had to identify and
analyze the survey bias that his response creates for a test in an
introductory statistics class.

------
kgroll
Edit: Just noticed that the Wolfram links break because of their syntax. HN
then worsens the problem, by shortening the displayed links with '...',
meaning copy/paste breaks! So I'm just removing the http prefix and you'll
have to copy/paste to view any of the graphs.

\---

This seems to disagree with the gist of the comic, but I think the answer to
the final part (largest dating pool) is 23 years old.

I arrived at that by doing the following, please correct me if you spot an
error along the way!

The dating range for any age, t, would be defined as:

    
    
      lower limit = .5t + 7
      upper limit = 2t - 14
    

This agrees with the example in the XKCD strip. The dating range for an 18
year old is from .5(18)+7 = 16 to 2(18)-14 = 22. Because this is linear, the
range will always be increasing with age.

Despite the range growing with age, we know that the proportion of singles is
decreasing with age. Sigh. That's where the other model comes in. The author
of this problem gives:

    
    
      S(t) = e^(-0.05*t)
    

That looks like this:
www.wolframalpha.com/input/?i=Plot[E^(-0.05+x),+{x,+85,18}]

I believe the largest dating pool would correspond with the greatest area
yielded by taking the definite integral of this function from .5t+7 (the lower
age limit) to 2t+14 (the upper age limit). To see this in pretty print, you
can visit this link: www.wolframalpha.com/input/?i=integrate+(E^(-.05
_x))+dx+from+(.5_ x%2B7)+to+(2*x-14)

Evaluating that for any age would give the area under the curve corresponding
to that age.

The next step, then, would be to find the maximum area for any age. To do
this, we should be able to take the derivative of that previous equation, and
set it equal to 0 in order to maximize it. Again, correct me if I'm wrong, but
for the result of that, I get:

    
    
      -2000(e^(-0.1t+0.7) - e^(-0.025t+0.35)) = 0
    

I plotted that to find that the max was located at age t = 23.

This graph illustrates the size of the dating pool corresponding to age along
the x axis:
www.wolframalpha.com/input/?i=Plot[-2000(e^(-0.1x%2B0.7)-e^(-0.025x%2B0.35)),+{x,+0,+100}]

Comments? Did I approach this totally wrong? Did I miss something along the
way? Does that seem reasonable?

~~~
gmichnikov
The upper age limit is 2t-14 (as you note earlier in your comment) rather than
the 2t+14 you mention later.

Integrating, you get -20(e^(-0.05(2x-14)) - e^(-0.05(x/2+7)))

The derivative (eliminating the constant) is: (e^0.7)
_(-0.1)(e^(-0.1x))+(e^-0.35)_ (0.025)(e^(-0.025x))

Wolfram gives about 32.5 as the root. You can plot the integral (try
www.coolmath.com/graphit) and mouse over to confirm.

------
snes
Next, everyone will be called a cheater and have to retake the exam because
they have read xkcd before.

------
cosmicray
if they use this one, does it become a recursive loop ? ... nerd sniping:
<http://xkcd.com/356/>

~~~
tw1st3dst33l
Personally, <http://xkcd.com/308/> is what I live my life by.

------
CUViper
I find it odd that the test's adaptation removes the first two words from
"standard creepiness rule: don't date under (age/2+7)". Is it objectionable to
refer to dating with large gaps of age as creepy?

~~~
waterlesscloud
Perhaps it's objectionable if you're a professor with a lot of hot students.

~~~
kleiba
I find it creepier when a professor's unwilling to cite a source accurately.

------
lgarron
We had an entire set of programming questions at ProCo (programming contest
held at Stanford for high school students) themed with XKCD comics last May:
<http://cs.stanford.edu/wiki/proco/PastContests/2010Problems>

------
die_sekte
Ideal dating pool seems to be around age 32.

I don't know how to optimize a function with an integral in R yet
(unsurprising, just installed it 20 minutes ago), therefore I can't give a
better answer. Now I want to learn R.

