A sequence of positive integers is given such that the sum of any $6$ consecutive terms does not exceed $11$. Prove that for any positive integer $a$ in the sequence one can find consecutive terms with sum $a$
Source: Belarusian MO 2023
Tags: combinatorics, Sequence
A sequence of positive integers is given such that the sum of any $6$ consecutive terms does not exceed $11$. Prove that for any positive integer $a$ in the sequence one can find consecutive terms with sum $a$