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Results tagged with puzzle
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user 12978
Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.
2
votes
A function that is defined everywhere but has unknown values
Hilbert's 10th problem.
Let $f$ be as follows. For every multivariable integer-coefficient polynomial $p$ (properly encoded as a natural number), let $f(p)$ encode an integer solution $\bar{x}=(x_1, …
- 6,287
2
votes
A function that is defined everywhere but has unknown values
Trivial Answers:
These probably aren't helpful but...
1) Randomness: Flip a coin repeatedly and let $f(n)$ be the $n$th flip. It is clearly unknowable in a heuristic sense. But it is also incomput …
- 6,287
2
votes
A function that is defined everywhere but has unknown values
Kolmogorov Complexity
This should actually be easy to explain. Fix a programming language like Java. Let $K(n)$ be the length of the shortest computer program (in number of ASCII characters for exa …
- 6,287