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Results tagged with puzzle
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user 12705
Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.
30
votes
Accepted
A puzzle about finding three points $(x,y)$, $(x,z)$ and $(y,z)$ in a subset of a square.
Let $S(x)=\{y\mid(x,y)\in S\}$ and $S^{-1}(y)=\{x\mid(x,y)\in S\}$, and let $\lambda_n$ denote the Lebesgue measure on $[0,1]^n$. We have
$$\begin{align*}
\int_S(\lambda_1S(x)+\lambda_1S^{-1}(y))\,dx …
- 47.3k
3
votes
Accepted
A simple language and systematic computations
I claim that $M(n)=n^{\Theta(n)}$.
The upper bound is easy: we can assume without loss of generality that an $n$-line program only uses variables $a_0,\dots,a_{n-1}$, hence there are only $n^2+2n$ po …
- 47.3k