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Home » Super Super Saiyan God: The Ultimate Form That DESTROYS Weaknesses! - Sterling Industries

Super Super Saiyan God: The Ultimate Form That DESTROYS Weaknesses! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Solution: We are to count the number of distinct circular arrangements of 12 pollen grains — 5 oak (O), 4 pine (P), and 3 birch (B) — such that no two birch grains are adjacent. All grains of the same type are indistinguishable. Arrangements are considered up to rotation (circular symmetry).

📌 We use the method for circular arrangements with non-adjacency constraints.

📌 In circular arrangements of indistinct objects, we fix one non-birch grain to eliminate rotational symmetry. However, since birch is the restricted type, its better to first arrange the non-birch grains and place birch in the gaps.

📌 These 9 grains create 9 possible gaps (between and around them) where birch grains can be placed. Since no two birch grains can be adjacent, we must place the 3 indistinct birch grains into distinct gaps, with at most one per gap.

📌 Number of ways to choose 3 distinct gaps out of 9:

📌 Now, for each such gap selection, the arrangement of the 9 non-birch grains (with indistinct types) can be uniquely ordered. The number of distinct linear arrangements of 5 Os and 4 Ps is:

📌 So total valid circular arrangements (with no two birch adjacent, fixing rotational symmetry by treating the circle via non-birch placement) is:

📌 But wait: in circular arrangements, fixing one non-birch (to break rotational symmetry) and arranging the rest relative to it is equivalent to the above method. Since the grains are otherwise indistinct by type, and we are counting distinct circular configurations up to rotation, the above count is valid.

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