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How to find all naturals $n$ such that $\sqrt{1 {\underbrace{4\cdots4}_{n\text{ times}}}}$ is an integer?

Relation between inclusion-exclusion principle and maximum-minimums identity

Probability of a substring occurring in a string

Question about members in sets

How many ways are there to distribute 5 balls into 3 boxes, under additional conditions?

Combinatorial Analysis: Fermat's Combinatorial Identity

Find the number of different colorings of the faces of the cube with 2 white, 1 black, 3 red faces?

There is a no set which every line meets the ball

Asymptotic estimation of $A_n$

The drawn diagonals divide the $N\times N$ board into $K$ regions. For each $N$, determine the smallest and the largest possible values of $K$.

Counting how many hands of cards use all four suits

Grouping items into groups

Proving the number of permutations $A,B\;$ with $n+1$ total cycles and $AB=(123\cdots n)$ is $C_n$

Sum of variables in graph optimum

How many $5$-digit numbers are there, so that $0,1$ and $2$ are NOT included, $3,4$ and $5$ have to be included

Expected value of the largest element of a subset

Number of binary trees with $N$ nodes

Number of distinct words with at least 2 $a$s, 1 $b$ and 1 $c$

New posts in combinatorics

Sum with binomial coefficients: $\sum_{m=1}^{k}\frac{1}{m^{2a}}\binom{k}{m}$ with constant a

Handshaking with no crossovers in minimum number of rounds: has this problem been studied?

How to find all naturals $n$ such that $\sqrt{1 {\underbrace{4\cdots4}_{n\text{ times}}}}$ is an integer?

Relation between inclusion-exclusion principle and maximum-minimums identity

Probability of a substring occurring in a string

Question about members in sets

How many ways are there to distribute 5 balls into 3 boxes, under additional conditions?

Combinatorial Analysis: Fermat's Combinatorial Identity

Find the number of different colorings of the faces of the cube with 2 white, 1 black, 3 red faces?

There is a no set which every line meets the ball

Asymptotic estimation of $A_n$

The drawn diagonals divide the $N\times N$ board into $K$ regions. For each $N$, determine the smallest and the largest possible values of $K$.

Counting how many hands of cards use all four suits

Grouping items into groups

Proving the number of permutations $A,B\;$ with $n+1$ total cycles and $AB=(123\cdots n)$ is $C_n$

Sum of variables in graph optimum

How many $5$-digit numbers are there, so that $0,1$ and $2$ are NOT included, $3,4$ and $5$ have to be included

Expected value of the largest element of a subset

Number of binary trees with $N$ nodes

Number of distinct words with at least 2 $a$s, 1 $b$ and 1 $c$