People who like this might also enjoy the similarly simple (yet unsolved) Collatz Conjecture:<p><a href="https://en.wikipedia.org/wiki/Collatz_conjecture" rel="nofollow">https://en.wikipedia.org/wiki/Collatz_conjecture</a>
When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable is a valid answer to a problem. I felt cheated(1) and the whole book lost a lot of its appeal.<p>In retrospect it may have actually undone some damage done by the school system where the solution space is usually very restricted.<p>Edit: (1) From what I remember it’s stated as find the sequence and not does such a sequence exist.
I have learn more geometry from trying to solve the unsolvable "squaring the circle" problem than all the Geom. classes I had in my life. For example: No one ever has told me in school that for all squares, the length of the diagonal equals The Square Root Of Two times the side of the square's, so for a square where the side is 1 meter, the diagonal will be Sq.Rt.o'2 meters (around 1,4 m), And I came to find that by myself doing the exercise of the unsolvable. Also, more recently early this year, I found that the diagonal/diameter of a Pentagon was the Cubic Root of 3, or this was the hexagon, and the heptagon was the S.q.rt.o'2 multiplied by C.rt.o'3 or something like this, the thing is that they follow a sequence, Its always something with the square and cubic roots of 2 and 3 and I guess 5 or 7 will appear later in the sequence for polygons with more sides, noting that for a "infinite sides 'polygon' " , which would be a circle, the number that relates the diagonal with the "'sides'", or in this analogy, the Perimeter , is Pi...Anyway, good exercises. p.s: I have remembered that back then I thought maybe Pi was Square Root of Infinity, and now just came to my mind that maybe would be the Infinite Root of something...But off course just joking thinking, but nice exercise.