Break open the number lock code from five hint clues. Each clue in the number lock puzzle includes a 3 digit code and digit and position information.
3 Digit Number Lock Code Puzzle With 493 in a Hint
Following are the five clues as hints:
Clue 1: Code 4 9 3: One digit is correct but in the wrong place.
Clue 2: Code 4 1 6: One digit is correct and in the right place.
Clue 3: Code 1 8 4: Two digits are correct but both are in the wrong places.
Clue 4: Code 9 6 2: One digit is correct and in the right place.
Clue 5: Code 8 5 7: One digit correct in the wrong place.
Break open the number lock code in a quick series of breakthroughs.
Time to solve: 10 minutes.
Challenge met in Breaking Open the 3 Digit Number Lock Code in a Quick Logic Chain
Solution in a Chain of Analysis based on common digit clues and position and digit correctness patterns.
Breakthroughs: All clues take part in logic analysis, but first breakthrough by Clues 1+2+3, positions of correct digits decided by Clues 2+5, and third correct digit confirmed by Clue 4.
Step 1. First couple of breakthroughs analyzing three clues in combination
By their common digit patterns, Clues 1, 2 and 3, if analyzed in combination should produce multiple breakthroughs:
Patterns:
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All three are positive clues with hint code digit (one or two) stated correct.
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Clues 1 and 2 clearly promise first breakthrough as both have 4 in same position but with differing position description.
Clues analyzed in combination:
Clue 1: Code 4 9 3: One digit is correct but in the wrong place.
Clue 2: Code 4 1 6: One digit is correct and in the right place.
Clue 3: Code 1 8 4: Two digits are correct but both are in the wrong places.
Logic analysis:
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Position and correctness conflict in Clues 1+2: correct digit 4 in same place, but stated in Clue 1 as wrongly placed and in Clue 2 in right place => Contradiction => digit 4 wrong confirmed => incorrect digit elimination in Clue 3 confirms two digits 1 and 8 right at one go.
Step 2. Positions of two correct digits confirmed by combined multiple clue analysis
Combined analysis of Clues 2 and 5 will confirm the positions of the correct digits.
Patterns:
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The clues are both positive with a single correct digit in their hint codes.
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The clues together include the secret code correct digits 1 and 8.
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Importantly, in one clue, correct digit position in its hint code is right and in the other wrong.
Clues analyzed in combination:
Clue 2: Code 4 1 6: One digit is correct and in the right place.
Clue 5: Code 8 5 7: One digit correct in the wrong place.
Logic analysis:
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Positional analysis: Clue 2 (4 1 6): One digit is correct and in the right place => correct digit 1 in middle confirmed => Clue 5: ( 8 5 7) : One digit correct in the wrong place =>1 occupying middle, 8 can only be in the rightmost place confirmed => Partial secret code: [ ? 1 8 ].
Step 3. Get the third correct digit by analyzing the right clue
Look for a positive clue with clue code digit as correct in correct position.
Pattern:
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In Clue 4, one digit is correct in its place. This will determine the third correct digit immediately.
Clue analyzed:
Clue 4: Code 9 6 2: One digit is correct and in the right place.
Logic analysis:
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Positional conflict: Clue 4 (Code 9 6 2), both 6 and 2 cannot be correct and in right place in middle and rightmost, as the positions are already occupied by 1 and 8 => 9 is third correct digit in leftmost position confirmed.
Solution: Secret code [ 9 1 8 ].
As all clues are used in the three-step logic chain solution, no verification needed. If you feel so, verify the solution against each clue.
What you learned: the strategy and digit pattern based techniques
1. All clues briefly analyzed to discover opportunities in digit+position patterns in multiple clues and helps in mapping the series of links in the sequential logic chain.
2. Position and correctness conflict: In a pair of clues, a correct digit is in same place in both hint codes, but position descriptions differ, creating conflict. This confirms the digit as incorrect.
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Example: In Clues 1+2, digit 4 leftmost in both, stated correct but position status differ. 4 identified as incorrect. By incorrect digit elimination, a necessary and routine practice, digits 1 and 8 confirmed correct in Clue 3 — three clues analyzed for a double breakthrough.
3. Positional analysis: In multiple clues, position of a digit is confirmed from position descriptions analyzed together.
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Example: Clues 2+5: In Clue 2, digit 1 is the only correct digit in right position in middle. In Clue 5, digit 8 being in its wrong leftmost position and middle position occupied by 1, digit 8 must be the rightmost. Partial code could be formed: [ ? 1 8 ].
4. Position pattern based technique: Positional conflict: In a clue, a digit claims a position already occupied by a correct digit in partial secret code.
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Example: In Clue 4 (Code 9 6 2), both 6 and 2 clash in positional claim with 1 in middle and 8 in rightmost. This confirm both wrong and third correct digit 9 in leftmost position.
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Solution: secret code [ 9 1 8 ].
The three-step quick analyses join into a short chain of logic — one deduction seamlessly merging with the next.
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