One of my favorite KöMaL problems (B. 4463): "In the Four-square Round Forest, trees form a regular triangular lattice. Is it possible to build a fence around a rectangular part of the forest such that the vertices of the rectangle are lattice points and the number of lattice points on the boundary of the rectangle is the same as in the interior?"
@jsiehler Is there a trick to this? I found a solution quickly by looking at small rectangle heights and finding a width that worked for one of the heights, but I wouldn't say there was any elegance to my reasoning.
@11011110 I like the problem partly because it's open to investigation like that. I've done the same problem with middle school students, and substituting a square grid for the triangular one, with 5th grade students. The more advanced student can change the "Is it possible" question to "Find all such rectangles, with proof." It's still not very hard, but it comes down to a finite (and small) number of possibilities in what I found to be an interesting way.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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