I read an interesting Science and puzzle book by Clifford Pickover one time. I forget the title, but the main topic was Black Holes. However, IN the last Chapter and elsewhere in the book, Pickover discussed all sorts of unsolved math problems, Chess piece problems, and other unsolved puzzles. For example solving open and closed tours of knights on the chess board, or using a 2,3 leaper, or 3/4/5 leaper instead of a knight, etc. One of the puzzles involved determining the thickness of an infinitely long, but infinitesimally thin roll of toilet paper when rolled up. There seems to be no solution to the problem and it doesn't make sense.
In one Chapter, he discussed how space itself becomes "Time-Like" in the presence of a Black Hole. That is all paths lead one way: Deeper into the black hole.
Turns out the guy is an atheist, so I don't really like his core beliefs, but even an atheist can be entertaining at times.
There was a section of calculating the first number which is an even power of 2, but contains three consecutive sixes "666" which his characters called "Apocalyptic Powers" and "Double Apocalyptic Powers" for six consecutive sixes in a number which is an even power of 2. He had a degree in computer programming, and discussed how to program a computer in C language to calculate such numbers. I found it fascinating.
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