You Need to Analyze More Than One Suitable Clue Together
Can you solve 3 digit number lock puzzle 158 in two steps of logic analysis? Given: 5 clues with hint codes and position-correctness information.
The 3 Digit Number Lock Puzzle with 158 in 5 Hint Clues
The five clues are:
Clue 1: Code 1 5 8: Two digits are correct and in the right places.
Clue 2: Code 1 5 0: One digit is correct and in the right place.
Clue 3: Code 8 4 7: Two digits are correct but both are in the wrong places.
Clue 4: Code 5 6 7: Two digits are correct but both are in the wrong places.
Clue 5: Code 5 8 1: Two digits are correct but both are in the wrong places.
Time to solve: 5 to 12 minutes.
Hint: Analyze multiple clues with common digits for assured breakthrough.
Solution to Crack Number Lock Puzzle 158 in Two Steps
Step 1: First breakthroughs based on common digit pattern in three clues
Clues 1, 2, and 4 with digit 5 common promise multiple breakthroughs.
Key patterns: Both Clues 1 and 4 are positive with two hint code digits stated correct and common digit 5.
First assured breakthrough by false assumption logic on 5.
Clue 1: Code 1 5 8: Two digits are correct and in the right places.
Clue 4: Code 5 6 7: Two digits are correct but both are in the wrong places.
Clue 2: Code 1 5 0: One digit is correct and in the right place.
- Clues 1+4: False assumption logic: Assume 5 wrong => four digits (1,6,7,8) correct in a 3 digit lock code => impossible => assumption wrong and 5 is the first correct digit in middle position (Clue 1).
- Additional conclusions (these are important):
- First: In Clue 2, digit 5 being correct, both 1 and 0 are wrong => in Clue 1, with 1 wrong, 8 is the second correct digit in rightmost place => partial secret code [ ? 5 8 ].
- Second: In Clue 4, the third correct digit must be one of (6 or 7) to occupy the leftmost position, and both have valid claims for the only vacant position.
This is the point when you need more clues.
Step 2: Eliminate candidates by testing possibilities for the third correct digit
Status: partial code [ ? 5 8 ] and one of 6 or 7 correct.
Analyze Clue 3 with correct digits 5, 8 and a pair of probable correct digits (4 and 7).
- Both (4 and 7) claim for the leftmost, but the correct digit can only be one of (6 or 7): common digit 7 satisfies both claims => 4 wrong => 7 is the third correct digit => secret code [ 7 5 8 ].
- Assert: 4 can’t be correct — because if 4 were correct, Clue 4 (5 6 7) would have only one correct digit (5), not two => X Contradiction.
To be sure, take the essential action: Verify the secret code 758 against all five clues, including the unused Clue 5.
Do it yourself for your satisfaction.
It is always a good practice not to depend on other's decisions: verify yourself for complete confidence.
Answer: 758.
What did you learn?
- Position and correctness analysis of positive clues with a digit common is the bedrock of all breakthroughs in solving number lock puzzles.
- False assumption logic applied on the common digit assures breakthrough.
- Example: In Clues 3+4, assumption of common digit 5 wrong led to a contradiction and proved 5 correct in its rightful middle position.
- Additional conclusions after a breakthrough are important: After a breakthrough, consider its implications for other clues. This can lead to quicker solutions later.
- Example: Digit 5 correct confirmed both 1 and 0 wrong in Clue 2 leading to confirmation of second correct digit 8 in rightmost in Clue 1.
- Example: More additional conclusion derived: either (6 or 7) is the third correct digit. This proved crucial for final breakthrough.
- Analysis of two probable correct digit pairs: an important technique that decides on one correct digit out of four.
- Example: Final breakthrough needed to identify the right Clue 3 giving a second probable correct digit pair (4 or 7) besides (6 or 7). The common digit 7 in the two pairs confirmed it as the third correct digit.
- Multiple clue analysis linked by common digit is the easiest way to discover correct digits.
- Example: This is established by the double breakthrough taken three clues together.
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