3,1,8一个号码正确,位置正确 3,7,9一个号码正确,位置不正确 8,6,3两个号码正确,位置都...

创建于:2025年4月24日

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问题

3,1,8一个号码正确,位置正确
3,7,9一个号码正确,位置不正确
8,6,3两个号码正确,位置都不正确
4,2,1号码都不正确
现在,推算出三位数密码

思考

Solving the puzzle logically

The user provided a puzzle with several clues to solve for a three-digit lock code.

I see that clue 4 tells me digits 1, 2, and 4 aren't in the code. With clue 1, we know that one of 3, 1, or 8 is correct and in the right spot. From that, I can discard 1 entirely and focus on possibilities for 3 and 8. I'll keep working through the clues to logically eliminate and narrow down the correct code.

Narrowing down possibilities

From my reasoning, since 1 isn't in the code, the only possible correct digits from clue 1 are 3 or 8. Whichever is correct must also be in the right position. If 3 is correct in position 1, then 8 can't be in the code. Looking at clue 3, I know that two digits are correct but in the wrong places, which suggests digits 8, 6, and 3 could be part of the code but in different positions. I need to keep narrowing this down logic by logic.

Reevaluating assumptions and concluding code

In this step, I’m analyzing clue 3 and dealing with contradictions. Since we’ve already ruled 3 out, we know 6 must be the correct digit that's misplaced. We also know the code contains 8 at position 3 and that 6 isn’t in position 2. This leaves position 1 for 6. The clues indicate only two digits from {8, 6, 3} are correct, so 3 is absent. From there, we know 8 and 6 must be in the code, fulfilling the clues. The code is coming together!

Thought for 27 seconds

回答

密码是 698

推理过程简要说明:

  1. “3 1 8:一个号码正确且位置正确”
    4 条线索表明 1 不在密码里(见第 4 条),因此这条线索中只有 3 或 8 可能正确且位置正确。

  2. “4 2 1:号码都不正确”
    排除 1、2、4。

  3. 若假设 3 在第一位正确,则与 “3 7 9:一个号码正确但位置不正确” 冲突(该线索要求没有数字在正确位置)。
    因此 3 不在密码里;由第 1 条可知 8 在密码里且位于第三位

  4. “8 6 3:两个号码正确,但位置都不正确”
    8 已确定在第三位,因此此线索中的 8(第一位)满足“位置不正确”;
    3 已被排除,所以另一个正确数字必须是 6,且 6 不能在第二位 ⇒ 6 在第一位

  5. 现在仅剩第二位未定。再看 “3 7 9:一个号码正确但位置不正确”
    3 已排除,7 若正确则不能在第二位,但第一位被 6 占,第三位被 8 占,不可能。
    ⇒ 正确数字为 9,且不得位于第三位 ⇒ 9 在第二位

最终得到三位数密码 698,并且可逐条验证满意所有线索。

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