Pigeonhole principle: From any ten two-digit numbers we can take two subsets with the same sum
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
144767
Picking integers satisfying a limit
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
142886
Find set with maximal cardinality given constraints
42744
Prove a number is even using the Pigeonhole Principle
96086
Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
39670
Use Pigeonhole to show of any set of $2^{n+1}-1$ positive integers is possible choose $2^{n}$ elements such that their sum is divisible by $2^{n}$.
43979
The total number of subsets is $2^n$ for $n$ elements
79984
Partition of ${1, 2, ... , n}$ into subsets with equal sums.
79342
Prove that any set of 2015 numbers has a subset who's sum is divisible by 2015
94295
Pigeonhole-principle with two choices
91485
Finding an uncountable chain of subsets the integers
84739
Amount of Number Combinations to Reach a Sum of 10 With Integers 1-9 Using 2 or More Integers
139935
Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
83518
Proving Two sets have same cardinality
98850
A positional number system for enumerating fixed-size subsets?
70439
Mapping two integers to one, in a unique and deterministic way