Show that if any ten of eleven integers can be split into two sets with the same total, then the eleven integers must be equal.
65780
After removing any part the rest can be split evenly. Consequences?
568
Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$.
104309
Pigeon-Hole Principle Common Sum
42744
Prove a number is even using the Pigeonhole Principle
150825
Is an empty set equal to another empty set?
24954
Prove that there are infinitely many integers of the form $111\ldots111$ that are multiple of $n$.
65764
Partitioning $\{1,2,\ldots,k\}$ into $p$ subsets with equal sums, where $p$ is prime
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
53670
Prove that it is possible to choose $100$ out of the first $200$ positive integers
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
68882
Path to Combinatorics Problem [$1.11$]
65978
How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
93572
How to determine if $n (n \geq 2)$ given numbers can be summed up to a certain number?
76405
Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
70439
Mapping two integers to one, in a unique and deterministic way
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
128716
Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side