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is purified and distilled water the same - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 $ a < b < c $ — strictly increasing order (one compound choice),

📌 But since $ a < b < c $, we have $ b - a > 0 $, $ c - b > 0 $, so:

📌 We list all such triplets and count how many satisfy $ 2b < a + c $.

📌 Lets proceed systematically. For each combination, compute $ a, b, c $, check $ 2b < a + c $.

📌 We can fix $ b $, then $ a < b $, $ c > b $, and search.

📌 Alternatively, note symmetry. For uniformly random $ a < b < c $, we analyze $ 2b - a - c $. We want $ 2b < a + c $.

📌 Then $ 2b < a + c = (b - d_1) + (b + d_2) = 2b + (d_2 - d_1) $, so:

📌 Thus, the condition $ 2b < a + c $ is equivalent to $ c - b > b - a $, i.e., the gap from $ b $ to $ c $ is larger than to $ a $.

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