81. Thieves and Gold Coins Four thieves steal some gold coins from the palace. At night, each thief divides the stolen coins into four equal parts, discarding one coin each time. After all four thieves have taken their share, how many coins did they originally steal? Added 28 April 2020 Show Solution Solution: They originally stole 63 coins. Here's the reasoning: 1. Let the initial number of coins be x. 2. The first thief divides the coins into four equal parts and discards one coin, so he takes (x-1)/4 coins, leaving 3(x-1)/4 coins. 3. The second thief does the same: divides the remaining coins into four equal parts and discards one coin, taking (3(x-1)/4 - 1)/4 coins, leaving 3(3(x-1)/4 - 1)/4 coins. 4. The third thief repeats this process, and so does the fourth thief. 5. After the fourth thief, there are no coins left, which means the initial number of coins x must satisfy the equation derived from these steps. 6. Solving this equation, we find that x = 63.
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