Can you solve number lock puzzle 143 with 5 clues? Each of the clues shows a 3 digit hint code stating how many are correct in correct or wrong position.
Can you solve number lock puzzle 143 with 5 clues? Each of the clues shows a 3 digit hint code stating how many are correct in correct or wrong position.
3 Digit Number Lock Code Puzzle With 143 in a Hint
Following are the five clues as hints:
Clue 1: Code 1 4 3: One digit is correct but in the wrong place.
Clue 2: Code 6 1 9: Two digits are correct but both are in the wrong places.
Clue 3: Code 2 7 5: One digit is correct and in the right place.
Clue 4: Code 9 0 3: One digit is correct and in the right place.
Clue 5: Code 8 1 6: One digit is correct in the wrong place.
Find the number lock code from the clues.
Time to solve: 12 minutes.
SOLUTION: Can You Solve Challenging Number Lock Puzzle 143?
Breakthroughs in succession are based on common digit correctness and position patterns in multiple clues.
Step 1. First breakthrough by position and correctness conflict
Clue choice and digit pattern:
Clues 1 and 4 have 3 common with conflicting position descriptions.
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Clue 1: Code 1 4 3: One digit is correct but in the wrong place.
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Clue 4: Code 9 0 3: One digit is correct and in the right place.
Logic analysis:
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Clues 1+4: 3 wrong by position and correctness conflict.
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Reason: 3 is a correct digit candidate, it occupies the same rightmost position in both clues, but a correct digit cannot be in its correct position in one clue and wrongly placed in the other. This creates the conflict.
Step 2. False assumption on common digit in two clues violates a third clue
Clue choice and digit patterns:
Clues 1 and 2 have 1 common. Assuming the common digit 1 is wrong leads to an immediate violation of Clue 3.
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Clue 1: Code 1 4 3: One digit is correct but in the wrong place.
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Clue 2: Code 6 1 9: Two digits are correct but both are in the wrong places.
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Clue 3: Code 2 7 5: One digit is correct and in the right place.
Logic analysis:
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Clues 1+2: Assume common digit 1 wrong => in Clue 2, both 6 and 9 are right => in Clue 1, digit 4 is the only correct digit => the secret code would have only the digits 4, 6 and 9 => a probable secret code [ 4 9 6 ] based on assumption "1 wrong".
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Clue 3 (2 7 5) has none of the three digits in this secret code => this violates the assumption, which must be wrong => 1 is the first right digit.
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Position analysis on 1 in Clues 1 and 2: For 1, leftmost position is wrong (Clue 1) as is the middle (Clue 2) => 1 must be the rightmost digit.
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Partial secret code: [ ? ? 1 ].
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Additional information: In Clue 2, the second correct digit must be one of 6 (in middle position) or 9 (in middle or leftmost position).
The partial secret code already satisfying Clue 1 and Clue 5, the clues won't play any role in further analysis.
Choice of the clues: Combined analysis of Clues 2, 3 and 4 for the final breakthrough is automatically determined.
Step 3. Position and correctness analysis cracks the secret code
Clue choice: Clues 2, 3 and 4 in combination.
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Clue 2: Code 6 1 9: Two digits are correct but both are in the wrong places.
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Clue 3: Code 2 7 5: One digit is correct and in the right place.
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Clue 4: Code 9 0 3: One digit is correct and in the right place.
Patterns of importance:
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9 common between Clues 2 and 4.
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6 (in middle) or 9 (in middle or leftmost) probable candidates for second correct digit (Clue 2).
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0 (in middle) or 9 ( in leftmost) probable candidates for third correct digit (Clue 4).
Logic analysis:
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Clue 3: Positional conflict: Digit 5 claims already occupied rightmost position => 5 wrong, 2 or 7 right in leftmost and in middle, respectively.
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Clue 3: False assumption: If 2 is correct in leftmost, secret code would be [ 2 0 1 ] from Clue 4 (9 wrong by positional conflict, 0 right in middle) => Violates Clue 2 (instead of two correct digits 1 is the only correct digit in its hint code 619) => assumption of "2 correct" is wrong => 7 correct in the middle => partial secret code [ ? 7 1 ].
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Clue 4: Positional conflict: 0 claims already claimed middle position => 0 wrong => 9 is the third correct digit in leftmost position.
Solution: secret code [ 9 7 1 ] satisfies all five clues.
If you wish, verify the code 971 against the clues.
Key Strategies You Learned:
1. Position and correctness conflict: When the same digit in same position is stated as probable "correct" in two clues but "wrongly placed" in one and "correctly placed" in the other, the conflict confirms the digit as incorrect.
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Ex: Digit 3 in Clues 1 (position rightmost, wrongly placed) and 4 (position rightmost, correctly placed) must be wrong.
2. False assumption violating a third clue: In two clues, assumption of a common digit wrong violates a third clue by the formation of a secret code with three digits none of which appear in the third clue.
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Ex: With assumption of 1 wrong in Clues 1 and 2 leads to three correct digits 4, 6 and 9 in the secret code none of which appears in Clue 3, proving the assumption wrong and 1 right.
3. Position analysis — Position confirmation by exclusion: Two positions for the correct digit in two clues stated to be wrong, confirms the remaining position correct for the digit.
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Ex: In both Clue 1 (1 4 3) and Clue 2 (6 1 9), position of correct digit 1 is wrong. Then, the correct digit must be in the remaining rightmost position in the secret code.
4. Positional Conflict: Once a digit's correct position in secret code is confirmed, it creates a positional claim. Any other digit claiming that same position in a subsequent clue must be incorrect.
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Ex: With 1 confirmed in rightmost position of secret code, the digit 5 claiming the same position in Clue 3 (hint code 275) must be incorrect.
5. Combined positional analysis of multiple clues: This deeper analysis reveals correct digits and correct positions by step-by-step application of other common pattern based techniques of false assumption and positional conflict.
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Ex: In combined positional analysis of Clues 2, 3 and 4, first positional conflict eliminated 5, next confirmed 7 correct in middle position by false assumption violating a third clue and finally identifying the third correct digit 9 by elimination of 0 in positional conflict for middle position.
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This deeper analysis of tightly linked logical conclusions in sequence, one after the next, cracked the secret code in a single analytical step.
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