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There are $2n+1$ people. For each $n$ people there is somebody who is friend with each of them. Prove there is a "know-them-all" person.

Help with combinatorial proof of identity: $\sum_{k=1}^{n} \frac{(-1)^{k+1}}{k} \binom{n}{k} = \sum_{k=1}^{n} \frac{1}{k}$

Number of total possibilities for an equation

Generating functions - deriving a formula for the sum $1^2 + 2^2 +\cdots+n^2$

Good upper bound for $\sum\limits_{i=1}^{k}{n \choose i}$?

How to prove indirectly that if $42^n - 1$ is prime then n is odd?

How to distinguish between combination and permutation questions?

When is $ 999\cdots$ a perfect square?

Proving $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$.

Prove that identity element is unique

The number of ways to order 26 alphabet letters, no two vowels occurring consecutively

Does triangulation have to be finite for Sperner's Lemma to Apply?

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

What is the position of the surviving mouse?

What is the probability that the digit sum of a randomly chosen integer between 0000 and 9999 is divisible by 5?

Set Interview Question, Any Creative Way to solve?

Is this graph Hamiltonian?

New posts in discrete-mathematics

There are $2n+1$ people. For each $n$ people there is somebody who is friend with each of them. Prove there is a "know-them-all" person.

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

Confused about adding cardinalities of sets as elements

What is the converse of this statement and is it true?

Help with combinatorial proof of identity: $\sum_{k=1}^{n} \frac{(-1)^{k+1}}{k} \binom{n}{k} = \sum_{k=1}^{n} \frac{1}{k}$

Number of total possibilities for an equation

Generating functions - deriving a formula for the sum $1^2 + 2^2 +\cdots+n^2$

Good upper bound for $\sum\limits_{i=1}^{k}{n \choose i}$?

How to prove indirectly that if $42^n - 1$ is prime then n is odd?

How to distinguish between combination and permutation questions?

When is $ 999\cdots$ a perfect square?

Proving $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$.

Prove that identity element is unique

The number of ways to order 26 alphabet letters, no two vowels occurring consecutively

Does triangulation have to be finite for Sperner's Lemma to Apply?

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

What is the position of the surviving mouse?

What is the probability that the digit sum of a randomly chosen integer between 0000 and 9999 is divisible by 5?

Set Interview Question, Any Creative Way to solve?

Is this graph Hamiltonian?