# Questions tagged [recreational-mathematics]

Mathematics done just for fun, often disjoint from typical school mathematics curriculum. Also see the [puzzle] and [contest-math] tags.

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### How is AC an angle bisector of $\angle PAB$?

Here is a problem involving tangent circles. Let $\omega$ be a circle with a diameter $PQ$. Another circle $t$ is tangent to $\omega$ at $M$ and also tangent to $PQ$ at $C$. Let $AB$ be a segment ...
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### Simplest expression for cos(1°) predating calculus

I was wondering what are the simplest formulas (or iterative process) to compute $\cos(1°)$ using only methods which predate calculus. To give a more precise meaning to my question, let me just recap ...
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### Recursive definitions and roots of polynomial equations

The following problem is given in Exercise 1.11 chapter 1 of "Galois Theory" by Ian Stewart. Let $P(n)$ be the number of binary strings of length $n$ in which consecutive ones occur in ...
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### How these circles are congruent?

Here is a problem involving curvilinear incircles and mixtilinear incircles. Let a triangle$\triangle$$ABC$ have circumcircle $\gamma$.It's A-Excircle tangency point at side$BC$ is $D$ Let $\gamma_1$ ...
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### Finding all natural $n$ such that $n^5+79$ has all digits same [closed]

Find all $n\in\mathbb{N}$ such that $n^5+79$ has all digits same. I worked with mod 3 and mod 9, because all the digits are same, but I couldn't move further. Although, I know $n=2$ is a trivial ...
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### HH vs. THTH Coin Toss

Alice tosses a fair coin until either she or Bob wins. Alice wins if she gets two consecutive heads (HH) and Bob wins if he gets Tails and Heads twice in a row (THTH). What is the probability that Bob ...
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### Visually intriguing unsolved problems which are easy to explain

I have come across a list of visual proofs which are wrong (Visually deceptive "proofs" which are mathematically wrong) visual proofs which are not wrong (Proofs without words) visually ...
I would like to be able to calculate the four parameters (A, B, C, D) for the sine curve $y=A\sin(Bt-C)+D$ given the generic boundary conditions that the value of the curve and its first derivative ...
### Size of a subset of $\mathbb{N}$
A subset $S\subset\mathbb{N}$ contains the numbers $5$ and $8$. If $n\in S$, then $7n-3$ and $7n+5$ are also in $S$ If $n\in S$, and $n=5m+4$, then $11m+9$ is also in $S$. Numerically, \$|S\cap[1,N]|=...