# Tagged Questions

Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

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### Collecting Stickers! Evaluate occurrence of duplicates?

The Sticker Collector You need to collect $n>1$ different Stickers. Each day you get one pack with $1$ random sticker until you don't collect at least one of each kind. * Each sticker ...
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### Definite integral problem of $\frac{x^n}{n!}$

I want to evaluate the following definite integral. $$\int_0^\infty\frac{x^n}{n!}dn$$ Where we have $n!=\Gamma(n+1)=\int_0^\infty t^ne^{-t}dt$ so that we can have $n\in\mathbb{R}$. I don't think ...
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### Formula for (word) frequency count

I searched for a mathematical formula for the description of (word) frequency count. Its definition would be: A word frequency count is a measure of the number of times that a word w occurs in ...
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### Monty Hall Problem extended

After seeing the popularity of the standard $3$ door problem, Monty thought to put a twist in the story. There are $N$ doors, $1$ car, $N-1$ goats. We need to choose any one of the doors. After we ...
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### Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
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### Minimizing the effort after toilet visit

We live together with 5 people (4 men and 1 woman) and the woman wants everyone to close the toilet after every turn (i.e. bring the seat and cover down, for smell reasons). To me this seems unfair. ...
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### Find all natural numbers of the form $2^n$ whose all digits are even

Find all natural numbers of the form $2^n$ whose all digits are even. For example: $2, 4, 8, 64, 2048$ (I believe they are the only such numbers). For $n \geq 11$, so far, I can prove that the last ...
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### Where is a good source for serious math (wall-size) posters?

Where is a good source for math wall posters that give glimpses of serious and beautiful mathematics? I'm a faculty member looking to find some wall posters (e.g. 2 ft x 3 ft) to hang in a handful of ...
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### What is the topology within a circle in order to map hypotenuses at the correct length? (see image)

Each slice of the triangle has a hypotenuse with a corresponding curve of equal length within the circle. What is the topology of the inside of the circle so that the curved lines equal the lengths ...