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Results tagged with recreational-mathematics
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user 172802
Applications of mathematics for the design and analysis of games and puzzles
34
votes
Accepted
Can an odd number of marbles jump to infinity?
With $5$ you can using the following moves:
..... ..... ..... ..... ..... ..... ..... ..oo. ...oo
..... ..o.. ..o.. ..o.. ..oo. ...oo ..ooo ..ooo ..ooo
.oo.. .oo.. .oo.. ..oo. .. …
- 10.6k
25
votes
1
answer
1k
views
Is there an open subset $A$ of $[0,1]^2$ with measure $>\frac{1}{100}$ that satisfies this p...
This is a crosspost from MSE.
Can we find for any given $\varepsilon>0$ an open subset $A\subseteq[0,1]^2$ with measure $>\frac{1}{100}$ such that, for any smooth curve $\gamma:[0,1]\to\mathbb{R}^2$ o …
- 10.6k
22
votes
Accepted
The $9$th tetration of $-\sqrt2$
This is not a huge coincidence: the idea is that the sequence $a_n={}^{n}(-\sqrt{2})$ has small norm until $n=6$, then it gets out of hand for $n=7$ ($a_7\sim-33+29i$), so that $a_8=e^{a_7\ln(-\sqrt{2 …
- 10.6k
7
votes
Accepted
Inspired by a card game: finding a path through $[\mathbb{N}]^n$
$[\mathbb{N}]^n$, with edges between $a,b\in[\mathbb{N}]^n$ if $\#(a\cap b)=n-1$, is an infinite graph in which all vertices have infinite degree. Moreover, for any two vertices $a,b$ in $[\mathbb{N}] …
- 10.6k