query: Possible number of subsets that must intersect of $\{1,2,3,...100\}$
positive_passages.docid: 17703
positive_passages.text: $S$ be a collection of subsets of $\{1,...,100\}$ ; any two sets in $S$ has non-empty intersection , what is the maximum possible value of $|S|$?
negative_passages.docid: 26919
negative_passages.text: Intersection of Connected Sets
negative_passages.docid: 1409
negative_passages.text: Proving that the given set has at most $2^{n-1}$ elements
negative_passages.docid: 6432
negative_passages.text: How many ways can N elements be partitioned into subsets of size K?
negative_passages.docid: 106455
negative_passages.text: intersection of infinite collection of finite sets?
negative_passages.docid: 108275
negative_passages.text: How do I count the subsets of a set whose number of elements is divisible by 3? 4?
negative_passages.docid: 146204
negative_passages.text: Subsets sharing at most $i$ elements
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 76381
negative_passages.text: Plain integer partitions of $n$ using $r$ parts
negative_passages.docid: 26569
negative_passages.text: Counting binary operations on a set with $n$ elements
negative_passages.docid: 96086
negative_passages.text: Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
negative_passages.docid: 2900
negative_passages.text: How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
negative_passages.docid: 144821
negative_passages.text: Number of ordered pairs of subsets
negative_passages.docid: 88628
negative_passages.text: Proving the total number of subsets of S is equal to $2^n$
negative_passages.docid: 13260
negative_passages.text: Choosing $101$ numbers from $\{1, 2, \dots , 200\}$.
negative_passages.docid: 53937
negative_passages.text: Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$.
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set