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Home » C. Gibbs Free Energy (ΔG) - Aurero

C. Gibbs Free Energy (ΔG) - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Solution: The code has 5 positions: _ _ _ _ _. The middle (3rd) character is fixed as B. We must choose 4 distinct letters from {A, B, C, D, E}, with B fixed in position 3, so the remaining 4 positions use the other 4 letters, but B is already placed, so we use A, C, D, E for the other 4 positions.

📌 We fix B in position 3. The remaining 4 positions (1st, 2nd, 4th, 5th) must be filled with the 4 other letters (A, C, D, E), each exactly once â so it's a permutation of 4 distinct letters.

📌 Number of such permutations: $ 4! = 24 $

📌 Thus, there are 24 valid codes.

📌 Question: A blockchain smart contract generates a token sequence using 4 gold tokens, 3 silver tokens, and 2 bronze tokens, where tokens of the same type are indistinguishable. How many distinct sequences of all 9 tokens can be arranged?

📌 Solution: We are arranging 9 tokens in total, where there are 4 identical gold, 3 identical silver, and 2 identical bronze tokens. The number of distinct permutations is given by the multinomial coefficient:

📌 rac{9!}{4! \cdot 3! \cdot 2!}

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