# Tagged Questions

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

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### Swap two integers in different ways

This is a famous rudimentary problem : how to use mathematical operations (not any other temporary variable or storage) to swap two integers A and B. The most well-known way is the following: ...
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### Computation of integral $\int_{0}^{1}\ln(p)\ln(1-p)p^{2}\,dp$

I want to compute this integral: \begin{equation*} J=\int_{0}^{1}\ln(p)\ln(1-p)p^{2}dp \end{equation*} It will be great if you can detail the proof. I tried to do change of variable it does not work,...
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### For how many seconds do I need to turn the pedal?

For how many seconds do I need to turn the pedal of a bike, so that the number of turns is equal to the value of my velocity in the given moment measured in km/h.
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### How to better compute this eta formula

In the question MRB constant proofs wanted , I gave the following excerpt from http://marvinrayburns.com/UniversalTOC25.pdf . . I accurately worked formula 44 in Matheamatica in the following code. ...
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### Finding every $n$ such that $n\times$ ('reverse' number of $n)=m^2$ such as $1584\times 4851={2772}^2$

Let $r(n)$ be the 'reverse' number of $n$ in the decimal system. For example, $r(1234)=4321$. Then, here is my question. Question : Can we find every $n(\in\mathbb N)$, which is not a square ...
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### Monotonically increasing path in a complete graph

Given a complete graph with n vertices such that all edge weights are distinct. Prove that we can find a monotonically increasing path of length n-1. I tried finding such a path by sorting the edges ...
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### What is the most mathematical flag? [closed]

I know it sounds stupid. But my professor asked us which is the most mathematical flag. As I know most of the flags of the countries are rectangle then what does he mean by most mathematical flag?