cpchen

Just as a tangent: what you posed is an example of what the magic community refers to as a problem (what the spectator sees). Magicians then try to come up with a method that satisfies all the constraints specified in the problem.

I'm going to be coy here: that's a classic in magic, with many possible solutions!

The classic recurrence is if you're choosing K elements out of N, it either has the first element (in which case you choose K-1 elements out of the remaining N-1) or it doesn't (in which case you choose K elements out of the remaining N-1), so:

N choose K = (N-1 choose K-1) + (N-1 choose K).

Also, if you sum (N choose K) for all values of K you get 2^N.

I enjoyed (the first 2/3 of) Steven Pinker's The Sense of Style. It includes examples of where prescriptivism fails and succeeds.

I don't have any studies, but check the wikipedia page for examples of Memory Championship winners using the method to, for example, memorize a deck of shuffled cards or a random sequence of digits. I bet Moonwalking with Einstein would have some references in the scientific literature.

There are techniques with better payoff and retention. Check the memory systems advocated by David Roth or Harry Lorayne, or the locus method (https://en.m.wikipedia.org/wiki/Method_of_loci)

In UC Berkeley, the 2 level means graduate student level.

I second Card College. Absolutely the highest standard in card magic pedagogy.