To solve the "Crack the Code" puzzle, we need to analyze each clue carefully and deduce the correct three-digit code. Let's break it down step by step.
Clues:
1.
3 6 8: One number is correct and in the correct place.
2.
3 8 7: No number is correct.
3.
2 7 6: One number is correct but in the wrong place.
4.
4 7 1: Two numbers are correct but in the wrong places.
Step-by-Step Analysis:
#### Clue 1:
3 6 8
- One number is correct and in the correct place.
- This means one of the digits (3, 6, or 8) is in the correct position.
#### Clue 2:
3 8 7
- No number is correct.
- This means none of the digits (3, 8, or 7) can be part of the code.
-
Elimination: We can eliminate 3, 8, and 7 from the code.
#### Updated Information:
- From Clue 2, we know the code cannot contain 3, 8, or 7.
- Therefore, the correct digit from Clue 1 (3, 6, or 8) must be
6 (since 3 and 8 are eliminated).
#### Clue 3:
2 7 6
- One number is correct but in the wrong place.
- Since 7 is eliminated (from Clue 2), the correct digit must be either 2 or 6.
- We already determined from Clue 1 that 6 is correct and in the correct place. Therefore, 6 cannot be in the wrong place here.
-
Conclusion: The correct digit is
2, but it is in the wrong place.
#### Clue 4:
4 7 1
- Two numbers are correct but in the wrong places.
- Since 7 is eliminated (from Clue 2), the correct digits must be 4 and 1.
- Both 4 and 1 are correct but in the wrong places.
Putting It All Together:
- From Clue 1, we know
6 is correct and in the correct place.
- From Clue 3, we know
2 is correct but in the wrong place.
- From Clue 4, we know
4 and
1 are correct but in the wrong places.
#### Positioning the Digits:
1.
6 is in the correct place. Let's assume it is in the middle position for now (we will verify later).
- Code so far: _ 6 _
2.
2 is correct but in the wrong place. It cannot be in the middle (where 6 is), so it must be in either the first or third position.
- Possible codes: 2 6 _ or _ 6 2
3.
4 and
1 are correct but in the wrong places. They cannot be in the middle (where 6 is), so they must occupy the remaining positions.
- If 2 is in the first position, then 4 and 1 must be in the third position and first position, respectively (but 2 is already in the first position, so this is not possible).
- If 2 is in the third position, then 4 and 1 must be in the first and second positions, respectively (but 6 is already in the second position, so 4 must be in the first position and 1 in the third position).
#### Final Code:
- First position: 4
- Second position: 6
- Third position: 1
Verification:
1.
3 6 8: One number correct and in the correct place. (6 is correct and in the correct place.)
2.
3 8 7: No number is correct. (None of 3, 8, or 7 are in the code.)
3.
2 7 6: One number is correct but in the wrong place. (2 is correct but not in the first position.)
4.
4 7 1: Two numbers are correct but in the wrong places. (4 and 1 are correct but not in the first and third positions, respectively.)
All clues are satisfied.
Final Answer:
\[
\boxed{461}
\]
Parent Tip: Review the logic above to help your child master the concept of crack the code math worksheet.
