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February 1, 2025 16:37
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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> | |
Alright, let's tackle this logic puzzle step by step. We have four friends: Anna, Bartosz, Cezary, and Danuta. Each is preparing for a distinct profession: archaeologist, bookkeeper, carpenter, and dentist. We're given a few key pieces of information: | |
1. **Bartosz will be a dentist.** | |
2. **Only one of these people is training for a profession that starts with the same letter as their name.** | |
3. **That person is not Anna.** | |
Our goal is to determine the professions of Anna and Danuta. | |
### Step 1: Assign Known Information | |
First, let's assign the known profession to Bartosz. | |
- **Bartosz:** Dentist | |
This leaves us with three professions to assign: archaeologist, bookkeeper, and carpenter. | |
### Step 2: Analyze the Second Clue | |
The second clue states that only one person has a profession that starts with the same letter as their name, and that person is not Anna. | |
Let's list the names and possible professions that start with the same letter: | |
- **Anna:** Archaeologist (both start with 'A') | |
- **Bartosz:** Bookkeeper (both start with 'B') | |
- **Cezary:** Carpenter (both start with 'C') | |
- **Danuta:** Dentist (both start with 'D') | |
However, we already know that Bartosz is the dentist, so Danuta cannot be the dentist. Therefore, the only possible person whose profession starts with the same letter as their name is: | |
- **Cezary:** Carpenter | |
This is because: | |
- Anna cannot be the one (as per the clue). | |
- Bartosz is already the dentist. | |
- Danuta cannot be the dentist (since Bartosz is). | |
- Therefore, Cezary must be the carpenter. | |
### Step 3: Assign Cezary's Profession | |
- **Cezary:** Carpenter | |
Now, we have two professions left: archaeologist and bookkeeper. | |
### Step 4: Determine Anna's Profession | |
Since Anna cannot be the one with a profession starting with 'A' (as per the clue), she cannot be the archaeologist. Therefore, Anna must be the bookkeeper. | |
- **Anna:** Bookkeeper | |
### Step 5: Assign Danuta's Profession | |
The only remaining profession is archaeologist. | |
- **Danuta:** Archaeologist | |
### Summary of Assignments | |
- **Anna:** Bookkeeper | |
- **Bartosz:** Dentist | |
- **Cezary:** Carpenter | |
- **Danuta:** Archaeologist | |
### Verification | |
Let's verify if all conditions are met: | |
1. **Bartosz is the dentist.** ✅ | |
2. **Only one person has a profession starting with the same letter as their name.** Cezary is the carpenter. ✅ | |
3. **That person is not Anna.** Cezary is not Anna. ✅ | |
All conditions are satisfied with these assignments. | |
### Final Answer | |
- **Anna:** Bookkeeper | |
- **Danuta:** Archaeologist |
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