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Carnegie Mellon: Alan and Danny's Puzzle Page

Alan Frieze and Danny Sleator, professors from Carnegie Mellon's School of Computer Science, are the hosts of this website of puzzles. Every few weeks, they post a new puzzle and a few weeks later, they post the solution and related references. The fairly advanced puzzles generally involve constructing an algorithm or a proof, and some also involve writing a computer program to solve them....

http://www.cs.cmu.edu/puzzle/index.html
Interactive Mathematics Miscellany and Puzzles

Alexander Bogomolny, a software developer and former mathematics professor, operates this educational and interesting Web site. His intention in creating the site is to help people "learn, if not math itself, then, at least, ways to appreciate its beauty." Although beauty is something most of us generally do not associate with the subject, the material manages to spark creative thinking by...

https://www.cut-the-knot.org/
The Grey Labyrinth: Puzzles

The Grey Labyrinth, which is paid for by visitor donations and maintained by a collection of volunteers, is an archive of puzzles from mathematicians, philosophers, and others. The editors challenge visitors to solve one of the rotating unsolved puzzles before the solution is posted online. Recently solved puzzles include a relativity game and exercises in geometry and probability. A survey on...

http://www.greylabyrinth.com/puzzles