The instructions, by the way, are at http://phdchallenge.com, which got cut off.

The classic coupon collector’s problem asks for the number of samples it takes to collect all coupon types from a sequence of coupons in which each of the \(k\) types of coupons has an unlimited number of copies.

Here is a different kind of problem: if there are limited copies of each of the \(k\) coupon types (say, \(d\) copies), how many samples does it take to collect \(t\) coupon types?

(Read the article)

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And some subtler ones:
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Here is a problem quoted from fakalin. A full deck of cards has 52 cards. Suppose 10 of them were face up and 42 were face down. You are in a dark room holding the deck. How do you rearrange the deck into two subdecks so that they have the same number of cards facing up?
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22/398, 29/271, 511

I read this in a document today:

All masculine and singular pronouns shall include the feminine, neuter and plural thereof, and vice-versa, wherever the sense of the language so requires.

Turns out Google latched onto somebody’s Yelp review.

“The physicist-run Prediction Company is an example of a company that has apparently extracted unusual profits from the market for over a decade. In contrast, economist-run companies like LTCM and Enron have gone belly-up. Being a physicist certainly doesn’t guarantee success … but if you are going to look for correlations in (market or any other) data then being a physicist might help.”

Joseph L. McCauley, writing in
Dynamics of markets: econophysics and finance

Trained Noses to Sniff Out Gulf Seafood for Oil

William Mahan bends over a bowl of raw shrimp and inhales deeply, using his left hand to wave the scent up toward his nose. Deep breath. Exhale. Repeat. He clears his palate with a bowl of freshly cut watermelon before moving on to raw oysters. Deep breath. Exhale. Repeat.

He’s one of about 40 inspectors trained recently at a federal fisheries lab in Pascagoula, Miss., to sniff out seafood tainted by oil in the Gulf of Mexico and make sure the product reaching consumers is safe to eat.

Oh god help us.