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A modestly fun probability question from AskMetaFilter: If you shuffle a standard deck of 52 cards, and draw them 2 at a time until the deck is exhausted, what is the expected number of pairs (two cards of the same value) that you will draw?

I haven't looked at the answers on AskMe; I long ago learned not to get drawn into any discussions of probability questions on the internet, ever.

Just found this browser-based twisty puzzle plaything.
Pretty for sure, but it'll take a while to get a feel for how comfortable the controls are.

Thanks, no, I didn't mean that. But seriously, thanks for the suggestion.

Probably Solution 

I haven't seen this before in general, and in particular, I haven't seen it in The Times.

I introduced \(k=\left(5/3\right)^x\) and deduced \(k^2-k-1=0\) leading to \(k=\left(1+\sqrt{5}\right)/2\) and so \(x=\log_{5/3}\left(\left(1+\sqrt{5}\right)/2\right)\).

My calculator says that's about 0.94 which agrees with my a priori prediction (intermediate value theorem) that there should be a single real root between 0 and 1, closer to 1.

I can't reason out why we traditionally say "quadric" surfaces, as opposed to saying "quadratic."

If you've never tried the simple puzzle of packing the twelve pentominoes into a rectangle, give it a try.

"Huh, audio's busted. There's a weird buzzy rattle under everything."

[horn sounds]

"Oh, it's a Bruckner symphony playing in the background."

My one request for our college's website redesign was: Please don't make the landing page full screen, high bandwidth, autoplaying, unpausable video.

Hahahaha. Oh well.

Yeah, that sounds exactly like my general area of research.

"Web of Science,.your article publish
The journal publishes original papers presenting new scientific results on breeding, genetics, physiology, pathology and production of primarily wheat, rye, barley, oat and maize."

JSTOR's search functionality is...

Teaching multivariable calculus again for the first time in quite a while. Since this means teaching about the vector cross product, it brings to mind one the strangest "connection between wildly disparate-seeming things" theorems I know of:

Do you have a favorite tiling of the plane? Which one?

"In this post, I am going to show you how to write Fizzbuzz in the programming language Fractran."

Our technology services department hosed nearly every mac on campus about a week before classes start. I got mine back with a new operating system and none of my applications or settings restored - just a vanilla image with my documents restored (handed over with a cheerful "this is fine, right? we upgraded the operating system for you! Why do you look upset?"). Use anything "weird" on your computer like a "compiler" or a "dot file?" You're on your own, pal.

<quote>About 12,800,000 results (1.89 seconds)
No results found for "concerto for horse and orchestra".</quote>

Should I be disappointed that this doesn't exist, or gleeful at the opportunity....

Building a trivalent graph of harmonic relations among major and minor triads.

If you take two unit squares stacked one atop the other, and rotate one through an angle of \(\theta\) about its center, the area in the intersection of the two squares is an octagon. I found it a pleasant exercise to express the area of the octagon in terms of \(\theta\).

In times of rapid change and constant uncertainty, it's comforting to know that Dror Bar-Natan's web page will, until the heat death of the universe, look just as it did when I was a happy, bright-eyed graduate student.

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