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Home » First term $ a = 1001 $ - All Square Golf

First term $ a = 1001 $ - All Square Golf

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Number of distinct permutations of {A,A,B,C}: $ \frac{4!}{2!} = 12 $

📌 Total: $4 \times 3 \times 12 = 144$ — correct.

📌 Total outcomes: $4^4 = 256$ — correct.

📌 So probability is $ \frac{144}{256} = \frac{9}{16} $? But $144/256 = 54/96 = 27/48 = 9/16$ — yes, simplifies to $ \frac{9}{16} $. But $9$ and $16$ coprime, so yes.

📌 Wait — but $ \frac{144}{256} = \frac{144 \div 16}{256 \div 16} = \frac{9}{16} $, but $16 \times 9 = 144$, $16 \times 16 = 256$ — yes.

📌 But $144/256 = 0.5625$, and $9/16 = 0.5625$, correct.

📌 But let’s double-check total favorable: is there overcount?

📌 No — we fix the repeated word, then choose two others, then arrange. Each sequence is uniquely generated.

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