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Home » This ‘Soul Eater Not’ Twist Will Make You Rethink Every Plot You Knew! - Portal da AcÃºstica

This ‘Soul Eater Not’ Twist Will Make You Rethink Every Plot You Knew! - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: Compute the average:

📌 So, the average length is $ \boxed{6} $ centimeters.Question: An archaeologist is analyzing 7 distinct artifacts found at an Inca settlement, and wishes to divide them into 3 identical storage containers such that each container holds at least one artifact. How many distinct ways can this be done?

📌 Solution: We are to partition 7 distinguishable artifacts into 3 indistinguishable non-empty containers. This is equivalent to finding the Stirling numbers of the second kind, denoted $ S(n, k) $, which count the number of ways to partition $ n $ distinguishable objects into $ k $ non-empty indistinguishable subsets.

📌 We need $ S(7, 3) $. The value of $ S(7, 3) $ can be computed using the recurrence:

📌 S(n, k) = k \cdot S(n-1, k) + S(n-1, k-1),

📌 with base cases $ S(n, 0) = 0 $ for $ n > 0 $, $ S(0, 0) = 1 $, and $ S(n, k) = 0 $ if $ k > n $.

📌 Using known values or computing step-by-step:

📌 $ S(1,1) = 1 $

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\frac{1}{k(k+1)(k+2)} = \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)...
The sum becomes:
\sum_{k=1}^{50} \left( \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)}...
Reindex the sums:
= \frac{1}{2} \left( \sum_{k=1}^{50} \frac{1}{k} \right) - \left( \sum...
Combine terms:
= \frac{1}{2} \left( 1 + \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} \ri...
= \frac{1}{2} + \frac{1}{4} - \frac{1}{2} - \frac{1}{51} + \frac{1}{2}...
\frac{1}{4} - \frac{1}{102} + \frac{1}{104} = \frac{1}{4} - \frac{52 -...
Final answer: $\boxed{\dfrac{1325}{5304}}$Question:

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