Question: How many of the 30 smallest positive integers are congruent to 2 (mod 5) in the context of tidal cycle intervals?

March 11, 2026

Question: How many of the 30 smallest positive integers are congruent to 2 (mod 5) in the context of tidal cycle intervals?

**How Many of the 30 Smallest Positive Integers Are Cong

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Solution: This is equivalent to partitioning 6 distinct compounds into 3 non-empty, unordered subsets (phases). The number of ways is the Stirling number of the second kind $ S(6, 3) $, multiplied by the number of ways to assign these subsets to 3 distinguishable phases (since phases are distinct, e.g., Phase 1, 2, 3).
First, compute $ S(6, 3) = 90 $. Then multiply by $ 3! = 6 $ to assign the subsets to phases:
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After each cycle, 80% of the current input becomes usable output, with a 10% loss meaning only 90% is processed effectively—but the yield is 80% of the original input mass. The usable output per cycle is 80% of the mass input. To reach 500 kg, solve for smallest integer n such that:

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