The image shows a code-breaking puzzle where you need to determine a three-digit code based on the given clues. The clues are:

1. 514: One number is correct and well placed.
2. 158: Two numbers are correct but wrongly placed.
3. 204: One number is correct but wrongly placed.
4. 102: One number is correct and well placed.

Let's analyze this step by step:

Step 1: Analyze the First Clue (514)

• One number is correct and well placed.
• This means one of 5, 1, or 4 is in the code and in the correct position.

Step 2: Analyze the Second Clue (158)

• Two numbers are correct but wrongly placed.
• 1, 5, or 8 are in the code, but none are in the correct position.

Step 3: Analyze the Third Clue (204)

• One number is correct but wrongly placed.
• 2, 0, or 4 are in the code, but the correct digit is not in its position.

Step 4: Analyze the Fourth Clue (102)

• One number is correct and well placed.
• 1, 0, or 2 is in the code and in the correct position.

Deduction Process:

1. From the first clue (514), since one number is correct and well placed, either 5, 1, or 4 is in the correct spot.

2. From the second clue (158), two numbers are correct but wrongly placed. This tells us that 1 is part of the code but not in the middle, and either 5 or 8 is in the code but not in the correct position.

3. From the third clue (204), one number is correct but wrongly placed. Since 2 cannot be in the correct spot (based on the fourth clue), and 4 was previously ruled out (because it didn’t match the well-placed number in the first clue), 0 must be in the code but not in the second position.

4. From the fourth clue (102), we know one number is correct and well placed. If 1 is correct and well placed, it would contradict the second clue because then the 1 wouldn't be wrong. Hence, 1 is not the well-placed number here; 0 must be well placed.

Thus, from clues:

• The second digit can't be 0 because of the third clue.
• The third digit can't be 1 based on the first clue and the third clue.

The most consistent conclusion is:

• The first digit is 2 (since it's not correctly placed in the third clue).
• The second digit is 0 (it fits all clues correctly placed).
• The third digit is 4.

Conclusion:

The correct code is 204.

Would you like further details or have any questions? Here are five related questions:

1. What would the result be if 0 were the first digit based on the given clues?
2. How would the code change if the first clue had two numbers correct and well placed?
3. Can there be another possible solution given a different interpretation of the clues?
4. How do logic puzzles like this relate to computer algorithms?
5. What is the process to systematically solve such puzzles without guesswork?

Tip: When solving logic puzzles, try eliminating possibilities step by step, which can lead to a clearer solution.