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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

65 votes

Tweetable Mathematics

Erdos: You can color edges between √2ᵏ vertices red/blue so no monochrome size k subgraphs (Pick a random coloring. It probably works)
5 votes

Special rational numbers that appear as answers to natural questions

This may not exactly qualify, because it's still only the conjectured answer to a question. The question: Consider all $2$-colorings of $\{1,\dots,n\}$. What is the minimum number of monochromatic $ …
23 votes

What are your favorite instructional counterexamples?

Two common misconceptions that students have about the concept of independence in probability are 1) Thinking "$X$ and $Y$ are independent" means "$X$ and $Y$ don't affect each other". 2) Thinking " …
123 votes
Accepted

If you break a stick at two points chosen uniformly, the probability the three resulting sti...

Here's what seems like the sort of argument you're looking for (based off of a trick Wendel used to compute the probability the convex hull of a set of random points on a sphere contains the center of …
Kevin P. Costello's user avatar
8 votes

Undergraduate Level Math Books

For discrete mathematics, I would recommend Van Lint-Wilson's "A Course in Combinatorics" as a good introductory text. It consists of 38 (in my edition) chapters that give (often largely self-contain …