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A puzzle problem from James Tanton that I enjoyed: Can the faces of 27 unit cubes be painted red/green/blue is such a way that they can be assembled (in different orientations) to make an all-red cube, an all green-cube, and an all-blue cube? ("All-red cube" means all the exposed faces are red, and all the blue and green faces are hidden.)

New math post on my blog: Many presentations of axiomatic set theory contain an error

New math post on my blog: All polynomials of degree 3 or greater factor over the reals

New math post on my blog: A little more about the pedagogy of what it means to be transcendental

New math post on my blog: In simple English, what does it mean to be transcendental?

Are you familiar with the term “recitation” which means “a small discussion class concentrating on material presented in a larger lecture; a section.”? (Please RT.)

“My big mistake about dense sets”: For forty years I believed something about dense sets that wasn't true. Thanks Noah Schweber!

“A simple dice-throwing game that seems hard to play” : start with a pool of _n_ points; choose a 4-, 6-, or 8-dided die, throw it, subtract from your points pool. If the pool reaches 0 exactly, you win; less than 0 you lose. What's the optimal strategy and its chance of winning?

Math Stack Exchange followup discussion:

“Why is the S combinator an S?” (Historical investigation; the S does not appear to have anything to do with substitution.)

“On having the right theorem”: every permutation of the English alphabet contains a subsequence of six letters in order. Dilworth's theorem squashes this flat.

“Stack Exchange is a good place to explain initial and terminal objects in the category of sets”

Also here's an example of a simple-seeming claim I said was obviously true, but was actually completely false:

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