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What are those floors doing here?

Source: India EGMO TST 2024/2

December 31, 2023
algebrafloorsSummationEgmo tst

Problem Statement

Given that a1,a2,…,a10a_1, a_2, \dots, a_{10} are positive real numbers, determine the smallest possible value of ∑i=110⌊7aiai+ai+1⌋\sum \limits_{i = 1}^{10} \left\lfloor \frac{7a_i}{a_i+a_{i+1}}\right\rfloor where we define a11=a1a_{11} = a_1.
Proposed by Sutanay Bhattacharya
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