List questions from extremal-combinatorics

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Subsets of a set with common elements between themselves

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Maximum cardinality of a set of subsets

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Let $ \mathcal{T}= \{A \subset \{1,2,\ldots,9 \} \ ; \ |A|=5 \}$. Find $n_{\min}$...

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Let $S$ be a subset of $\{1, 2, \dots , 2019\}$ such that no two members of $S$ differ by 1, 2 or 9. What is the upper bound of the size of $S$?

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Maximum number of triangles given fixed number of edges

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$A_1,A_2,...,A_k\subseteq \{1,2,...,11\}$ are such that for any three of them at least two are not comparable by inclusion. What is a maximum of $k$?

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We have $n$ charged and $n$ uncharged batteries and a radio which needs two charged batteries to work.

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Arrange the numbers in the given rectangular blocks

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List Question

Identify a truth-teller among a group of truth-tellers and (honest) liars.

Optimizing a winning strategy for a quick tabletop game

Subsets of a set with common elements between themselves

Maximum cardinality of a set of subsets

Let $ \mathcal{T}= \{A \subset \{1,2,\ldots,9 \} \ ; \ |A|=5 \}$. Find $n_{\min}$...

Let $S$ be a subset of $\{1, 2, \dots , 2019\}$ such that no two members of $S$ differ by 1, 2 or 9. What is the upper bound of the size of $S$?

Sum and minimum in $3\times 3$ table

Optimization problem for routes

Relation between maximum matching of a graph and its complement

Maximum number of triangles given fixed number of edges

$A_1,A_2,...,A_k\subseteq \{1,2,...,11\}$ are such that for any three of them at least two are not comparable by inclusion. What is a maximum of $k$?

We have $n$ charged and $n$ uncharged batteries and a radio which needs two charged batteries to work.

Arrange the numbers in the given rectangular blocks

Small & Balanced family of sets

Allocating balls among boxes under specified conditions

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