New posts in combinatorics

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

combinatorics recreational-mathematics chessboard

Simplify $\sum \limits_{k=0}^{n} \binom{n}{k} 2^{\sqrt{k}}$

combinatorics binomial-coefficients

Placing numbers $1,2,...,7$ on an infinite square grid with constraint on each $3 \times 3$ block

What is the probability that a red ball is chosen before the black ball?

probability combinatorics

Find the coefficient of $x^{20}$ in $(x^{1}+⋯+x^{6} )^{10}$

combinatorics multinomial-coefficients

In how many ways can we partition a set into smaller subsets so the sum of the numbers in each subset is equal?

combinatorics combinations

Place $8$ rooks on a $10\times 10$ board.

How to evaluate $1 - \frac{\binom{n^2}{1}}{\binom{n+1}{1}} + \frac{\binom{n^2}{2}}{\binom{n+2}{2}} - \frac{\binom{n^2}{3}}{\binom{n+3}{3}} + ..$

combinatorics binomial-coefficients

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

combinatorics discrete-mathematics graph-theory recreational-mathematics

Can this be proved using Combinatorics or generating functions?

combinatorics summation binomial-coefficients generating-functions combinatorial-proofs

Are these two binomial sums known? Proven generalization to the Hockey Stick patterns in Pascal's Triangle

combinatorics summation binomial-coefficients

Given any nine numbers, prove there exists a subset of five numbers such that its sum is divisible by $5$.

combinatorics number-theory combinations

Meeting of people.

combinatorics graph-theory contest-math

Find the number of $n$ husband's placing

combinatorics inclusion-exclusion

In how many ways can five letters be posted in 4 boxes?

Number of strings, when each character must occur even times

What's the proof of correctness for Robert Floyd's algorithm for selecting a single, random combination of values?

combinatorics algorithms

What is the total possible combinations for an two dice throw.

combinatorics combinations

Intuitively understanding $\sum_{i=1}^ni={n+1\choose2}$

combinatorics soft-question summation intuition

How many different dice exist? That is, how many ways can you make distinct dice that cannot be rotated to show they are the same?

combinatorics dice