To find all subsets contain 7 elements from the set $ [{1, 2, ..., 14} ]$ such that the sum of the elements is divisible by 14

Asked Oct 02 '23 at 13:14

Active Oct 03 '23 at 05:34

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anyone can help solve this problem?

How many subsets contain 7 elements from the set $[ {1, 2, ..., 14}]$ such that the sum of the elements is divisible by 14

edited Oct 03 '23 at 05:34

Asaf Karagila

asked Oct 02 '23 at 13:14

Idham Muqoddas

What have you tried so far? – Chris Lewis Oct 02 '23 at 13:16
@ChrisLewis I have no idea – Idham Muqoddas Oct 02 '23 at 13:22
2

If you don't show any ideas, this question will probably be deleted. The easiest method is to code it. As a hint, though, try generalising: let $f(n)$ be the number of subsets of ${1,...,2n}$ whose sum is divisible by $2n$. Work out $f(n)$ for some small $n$. If you see a pattern, great; try to prove it. If not, try searching on OEIS for the sequence so you can read about it. – Chris Lewis Oct 02 '23 at 13:35
Since $14 = 2 \cdot 7$, you should try to determine conditions for divisibility by both $2$ and $7$. – N. F. Taussig Oct 03 '23 at 07:24

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