Has anyone figured out yet whether Snaky is a winner or loser in generalized ticktacktoe? It looks like the question is still open, but if anyone has any definitive sources...

Good Saturday morning calculus challenge: Evaluate \[\sum_{n=1}^\infty \frac{\cos(n)}{n}\] and \[\sum_{n=1}^\infty \frac{\sin(n)}{n}\] in exact terms.

Does anyone know any modern 3-player games (probably card or board games) that use Skat's characteristic structure, where the strongest player, determined by bidding, must defeat the cooperative play of the other two?

(perhaps the best tip comes from mst3k: I should really just relax.)

After $bigint years, I *still* find it difficult to make a good 2-hour final for a calculus class. I think I end up with decent ones, but I spend unconscionable amounts of time designing, balancing, trimming, simplifying, ordering, usf, usw.

I took a look around to see what tips & tricks I could steal for composing good calculus tests, and there's either very little on the web, or it's just too hard to find because it's buried by tips on *taking* (mostly standardized) calculus tests.

More Substantial Hint 

Hint 

Puzzle problem: Suppose \(A_1, A_2, \ldots, A_n\) are finite sets, and each \(A_i\) contains an odd number of elements. Prove that there is a set \(S\subseteq \left\{1, 2, \ldots, n\right\}\) such that \(\displaystyle\sum_{i\in S} \left|A_i \cap A_j\right|\) is odd for every \(j\in \left\{1, 2, \ldots, n\right\}\).

Today I learned...

NAME
comm -- select or reject lines common to two files

I say it is flat out wrong because the function preserves the non-integer distance between, e.g., 1.03 and 1.02.

sites.math.washington.edu/~reu

p45 of the PDF asserts: "there are many transformations of [the real number line] onto itself which preserve some distances and not others. (Move all the integer points one unit to the right, the others one unit to the left – only the integral distances are preserved."

This seems flat-out wrong – am I missing something? If it is as wrong as it seems, can anyone figure out what the author(s) might have been thinking?

I've seen lots of fractal zooms, but the transformation used in this one to make it appear as a "scroll" rather than a "zoom" is mathematically interesting:
youtube.com/watch?v=7EHB3ty-A_

I have a jar containing 24 tea bags, which come in pairs. When I want to make a cup of tea, I reach into the jar and pull a random bag out. If it's a single bag, I jot down 'S' (and make my cup of tea). If it's part of a pair, I rip it, put the other bag back in the jar, and jot down a 'P'. By the time the jar is empty, I have jotted down a 24-letter string of S's and P's such as PPPPPPSSPPPSSPPPSSPSSPSS. How many such strings are possible? (Generalize 24 to 2n if you're so inclined.)

Is there any even number greater than 12 which can be written *in only one way* as a sum of two primes?

Here's a fun sequence to think about (in Python 'cause that's what our CS lab is using):
def fn(x):
y=1;
while (int(y*(x/y-x//y)) == x%y):
y = y+1
return(y)

for x in range(1,256): print(fn(x))

For my 100th toot, I have a new puzzle page to introduce: "Port-and-Sweep Solitaire!" I wrote about it previously for Math Horizons, but it's so much better experienced in an interactive format:

homepages.gac.edu/~jsiehler/ga

Check the bottom of the page for further links.

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