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Home » Alternatively: number of ways to partition 4 labeled items into two unlabeled pairs: - Crankk.io

Alternatively: number of ways to partition 4 labeled items into two unlabeled pairs: - Crankk.io

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 5A glaciologist measures that a glacier retreated 120 meters over the first 4 years of observation and then accelerated to retreat 210 meters over the next 3 years. If the acceleration continues linearly (i.e., the annual retreat increases by a constant amount each year), and the pattern continues, how many meters will the glacier retreat in the next 5 years?

📌 The average annual retreat in the first 4 years is 120 / 4 = 30 meters/year.

📌 In the next 3 years, the retreat was 120 → 210 meters over 180 days, or using finite differences, we analyze the *annual* retreat increments.

📌 Let the annual retreat amounts be: Year 1–4: ?, ?, ?, ?; Year 5: A, Year 6: B, Year 7: C.

📌 But since the acceleration is linear, model the *annual retreat* as a sequence with constant second difference.

📌 Let the retreats (in meters/year) for the 5 years be: $ a, a+d, a+2d, a+3d, a+4d $.

📌 But the first 4 years total 120: $ a + (a+d) + (a+2d) + (a+3d) = 4a + 6d = 120 $

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