Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 761. (November 2019)

A. 761. Let $\displaystyle n \ge 3$ be a positive integer. We say that a set $\displaystyle S$ of positive integers is good if $\displaystyle |S| = n$, no element of $\displaystyle S$ is a multiple of $\displaystyle n$, and the sum of all elements of $\displaystyle S$ is not a multiple of $\displaystyle n$ either. Find, in terms of $\displaystyle n$, the least positive integer $\displaystyle d$ for which there exists a good set $\displaystyle S$ such that there are exactly $\displaystyle d$ nonempty subsets of $\displaystyle S$ the sum of whose elements is a multiple of $\displaystyle n$.

Proposed by Aleksandar Makelov, Burgas, Bulgaria and Nikolai Beluhov, Stara Zagora, Bulgaria

(7 pont)

Deadline expired on December 10, 2019.

### Statistics:

 7 students sent a solution. 7 points: Weisz Máté. 3 points: 2 students. 1 point: 4 students.

Problems in Mathematics of KöMaL, November 2019