I need this kind of examples to motivate my friend to study mathematics. When he was a high school student, he is really good at math, but since he went to college (he majors in Math), he became unmotivated and lazy. He's always complained that higher mathematics is too abstract and therefore, not fun anymore. (This is partly because math textbook written in Vietnamese is so boring with monotonous theorem-proof-theorem-... pattern, without any interesting examples and problems). However, my friend is very enthusiastic about solving puzzles and elementary math problems. So, could you give me some examples of puzzles that require some deep math to solve, which illustrate my belief that "clever and quick is not enough, deep is more important"?. I hope I can make him stop showing off and start studying math seriously.
Some good examples I know are:
- Instant Insanity puzzle
- Sam Loyd's 15-puzzle
- Lights out Puzzle (This puzzle can be solved by trial-and-error, but to know which configuration is solvable requires linear algebra).
I do not ask for seemingly elementary problems that turn out to be open for a long time (like Fermat's last theorem). I need examples that I can explain the solution to him.