Given the set $A=\{1,2,\dotsc,14\}$, find all subsets of $7$ elements that sum to a multiple of $7$.
134921
Find the number of all subsets of $\{1, 2, \ldots,2015\}$ with $n$ elements such that the sum of the elements in the subset is divisible by 5
116251
Number of distinct total orders on a set
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
104527
Prove that there are two subsets of any cardinality-10 subsets of $\{1,2\dots,106\}$ that sum to the same number
78163
Hint for problem on $4 \times 7$-chessboard problem related to pigeonhole principle
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
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?
6679
Counting number of subsets which contain a specific element
57822
Number of ways to choose two disjoint subsets of a set
126888
How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
1401
$\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation
55840
Number of functions from n-element set to {1, 2, …, m}
158671
Cardinality of a set that consists of all existing cardinalities
44214
The number of subsets of a set of cardinality $n$
79984
Partition of ${1, 2, ... , n}$ into subsets with equal sums.
57746
Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
31708
Divisibility criteria for $7,11,13,17,19$