A type of question that I incorporated into my 100-level discrete math course. I made about eight of these. I think it was a good addition. (They often functioned as a clue for the following question, which would entail coming up with one's own counting strategy for some problem)

\(n + (n+1) + (n+2) + \cdots + (2n-1)\)
\(= 1+4+7+\cdots+\left(3n-2\right)\)

These new journals are getting rather niche lately, it seems.

An enjoyable problem (104.B) from the latest Mathematical Gazette: A regular 7-gon is inscribed in the unit circle, with one vertex at (1,0). Find the equations of the two parabolas, symmetric across the x-axis, which pass through the vertices of the heptagon as shown.

All I can come up with for an animation today is this little inchworm guy.

While this isn't quite what @christianp asked for in his recent post, it's still pretty enough in its own way.

A design for coloring, if you're in to that sort of thing. Based on the orbit of a single point under the action of two rotation groups with different centers.

O is an interior point in the triangle 10, 26, and 36 units away from the three vertices respectively. Determine the side lengths a, b, and c, given that they are integers.

Divide the small, yet verdant state of Moosylvania (green, in the map below) into two congruent regions.

Three-regular, each 5-bit label appears exactly once, each vertex is the sum (xor) of its neighbors.


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