Newbetuts

In a club with 99 people, everyone knows at least 67 people. Prove there's a group of 4 people where everyone knows each other

What are $x$, $y$ and $z$ if $\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y} = 4$ and $x$, $y$ and $z$ are whole numbers?

If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?

Find the best strategy for a card game

How to minimise the cost of guessing a number in a high/low guess game?

Conjecture related to Lychrel numbers

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Euler's identity in matrix form

Does there exist a tool to construct a perfect sine wave?

A BDMO functional equation problem.

What does it mean to be $0.9-$Dimension?

Deriving Taylor series without applying Taylor's theorem.

Two players placing coins on a round table with the goal of making the last move [duplicate]

Which jigsaw pieces fit to make a create a square?

Ten soldiers puzzle

How many bishops can be placed on a $m \times n$ chessboard?

New posts in recreational-mathematics

Overlapping circles covering polygon

Number theory fun problem

Independence problem: one rook and maximum number of knights on the chessboard $8 \times 8$

The case of Captain America's shield: a variation of Alhazen's Billard problem

In a club with 99 people, everyone knows at least 67 people. Prove there's a group of 4 people where everyone knows each other

What are $x$, $y$ and $z$ if $\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y} = 4$ and $x$, $y$ and $z$ are whole numbers?

If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?

Find the best strategy for a card game

How to minimise the cost of guessing a number in a high/low guess game?

Conjecture related to Lychrel numbers

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Euler's identity in matrix form

Does there exist a tool to construct a perfect sine wave?

A BDMO functional equation problem.

What does it mean to be $0.9-$Dimension?

Deriving Taylor series without applying Taylor's theorem.

Two players placing coins on a round table with the goal of making the last move [duplicate]

Which jigsaw pieces fit to make a create a square?

Ten soldiers puzzle

How many bishops can be placed on a $m \times n$ chessboard?