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Home » \( n(n + 1) = 420 \) - Appfinity Technologies

\( n(n + 1) = 420 \) - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Since the roles are indistinguishable, we simply count the distinct groups of 3. Therefore, the number of different councils that can be formed is:

📌 A researcher is analyzing the distribution of 6 unique artifacts into 4 indistinguishable storage bins. How many distinct ways can the artifacts be distributed if each bin can hold any number of artifacts?

📌 This is a classic problem of distributing distinguishable objects (artifacts) into indistinguishable bins. The number of ways to distribute \( n \) distinguishable objects into \( k \) indistinguishable bins is given by the sum of Stirling numbers of the second kind, \( S(n, k) \), summed for \( r = 1 \) to \( \min(n, k) \):

📌 \sum_{r=1}^{\min(6,4)} S(6, r)

📌 We calculate each relevant Stirling number:

📌 \( S(6, 1) = 1 \) (all artifacts in one bin)

📌 \( S(6, 2) = 31 \) (two non-empty bins)

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