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February 1, 2025 16:15
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o3-mini-jobs
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<USER> | |
### 5. Four Friends | |
Anna, Bartosz, Cezary, and Danuta are four friends. Each of them is preparing for a specific profession: archaeologist, bookkeeper, carpenter, and dentist. It is known that Bartosz will be a dentist. Only one of these people is training for a profession that starts with the same letter as their name, and that person is **not** Anna. | |
**What professions did Anna and Danuta choose?** | |
<ASSISTANT> | |
We are given four friends and four professions: | |
- **Friends:** Anna, Bartosz, Cezary, Danuta. | |
- **Professions:** archaeologist, bookkeeper, carpenter, dentist. | |
The information provided is: | |
1. **Bartosz will be a dentist.** | |
2. **Only one person’s profession starts with the same letter as their name, and that person is not Anna.** | |
Let’s analyze the possibilities: | |
### Step 1. Identify the Possible “Letter-Matching” Cases | |
A profession “matches” a friend if the initial of the friend’s name is the same as the initial of the profession. | |
- **Anna:** Could match if she were an **archaeologist** (A vs. A). | |
- **Bartosz:** Would match if he were a **bookkeeper** (B vs. B), but we know he is a dentist. | |
- **Cezary:** Would match if he were a **carpenter** (C vs. C). | |
- **Danuta:** Would match if she were a **dentist** (D vs. D), but dentist is taken by Bartosz. | |
Thus, the only possibilities for a matching pair are: | |
- Anna as archaeologist, or | |
- Cezary as carpenter. | |
### Step 2. Apply the Clue About Only One Matching and It’s Not Anna | |
The clue states that **only one person** has a matching initial, and that person is **not Anna**. | |
- If Anna were an archaeologist, she would be the matching case. That would violate the condition because the matching person cannot be Anna. | |
- Therefore, **Anna cannot be the archaeologist**. | |
Thus, the matching case must be **Cezary as a carpenter**. | |
### Step 3. Determine the Professions for Anna and Danuta | |
So far, we have: | |
- **Bartosz:** Dentist (given). | |
- **Cezary:** Carpenter (to satisfy the matching condition). | |
That leaves the two remaining professions: **archaeologist** and **bookkeeper** for Anna and Danuta. | |
Since Anna cannot be archaeologist (because that would be a match for her), she must be the **bookkeeper**. | |
That means Danuta must be the **archaeologist**. | |
### Final Answer | |
- **Anna** is the **bookkeeper**. | |
- **Danuta** is the **archaeologist**. |
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