Given: 5 clues, each with a hint code and digit and position correctness information. Crack the minimal step solution to the 3 digit number lock puzzle 106.
Challenge: Crack the Code for Number Lock Puzzle with 106 in Minimum Steps: The Puzzle
Clue 1. Code 0 8 5: One digit is correct but in the wrong place.
Clue 2. Code 1 0 6: Two digits are correct and in the right places.
Clue 3. Code 1 2 4: Two digits are correct and in the right places.
Clue 4. Code 8 0 4: Two digits are correct and in the right places.
Clue 5. Code 9 7 4: One digit is correct and in the right place.
Solve the puzzle using minimum number of clues in minimum steps.
Time to solve: 5 minutes.
Hint: Use the common digit patterns in multiple clues to identify incorrect and correct digits.
Minimum Clue, Minimum Step Solution to the 3 Digit Number Lock Puzzle 106 with 5 Clues
First step is always to identify a correct or an incorrect digit.
Step 1: Identify a Correct Digit Using Multiple Clues and False Assumption Based Reasoning
Positive Clues 3 and 4 with common digit 4 (Positive clue: Digits and positions descriptions all correct) provide the first breakthrough.
Clue 3. Code 1 2 4: Two digits are correct and in the right places.
Clue 4. Code 8 0 4: Two digits are correct and in the right places.
- Both clues share digit 4 in the rightmost position.
- False assumption based reasoning: Suppose 4 is incorrect. Then, for Clue 3, the two correct digits must be both 1 and 2, and for Clue 4, the two correct digits must be 8 and 0. This would imply that four digits (1, 2, 8, 0) are correct, but the code only has three digits. This is impossible.
- Conclusion: Digit 4 must be correct and in the rightmost position (as stated in both clues).
Partial code formed: [ ? ? 4 ].
Step 2: Eliminate a Key Incorrect Digit by Positional Conflict in Digit Patterns of a Suitable Clue
Look for a clue having a correctly placed digit in the rightmost position already occupied by 4 in the partially formed code.
Clue 2. Code 1 0 6: Two digits are correct and in the right places.
- Positional conflict: Since the rightmost digit is already confirmed as 4 (from Step 1), digit 6 (in the rightmost position in Clue 2) cannot be correct. Thus, 6 is incorrect.
- The two correct digits in Clue 2 must be 1 and 0, both in their right places in the lock opening code.
- This means digit 1 is in the leftmost position and digit 0 is in the middle position.
Solution: Lock opening code: [ 1 0 4 ].
Solution in two steps using three clues - a minimum clue, minimum step solution.
Verify the lock opening code against the unused Clues 1 and 5.
Clue 1. Code 0 8 5: One digit is correct but in the wrong place.
- Digit 0 of solution code is in the hint code and as described in the clue, it is in a wrong place. Code verified.
Clue 5. Code 9 7 4: One digit is correct and in the right place.
Digit 4 in solution code is in its place in the hint code as well. Code verified.
Lessons Learned from the Solution
- As a first step, always identify a correct or an incorrect digit, which helps later to identify the correct digits.
- Use pattern of common digits in multiple clues: If identification isn't possible from a single clue (which usually is the case), look for more than one clue with at least one digit common.
- Positive Clues 3 and 4 both had digit 4 in the same position. Analysis of this pair of clues helped to identify the first correct digit.
- Assuming 4 was incorrect in Clues 3 and 4 quickly showed an impossibility, forcing the correct conclusion.
- Forming the partial code [ ? ? 4 ] streamlined further deduction by blocking the rightmost position.
- Once 4 was fixed in the rightmost position, Clue 2 (which had 6 as the rightmost) immediately revealed that 6 must be incorrect, allowing us to deduce the positions of the rest of correct digits 1 and 0.
- Only two steps were needed to crack the code, demonstrating the power of combining clues and leveraging positional conflicts.
Overall, it has been an exercise of choosing the most suitable combination of clues individually or together for breakthroughs.
Pattern based logic analysis on common digits in suitably chosen multiple clues ensured the minimum clue, minimum step solution with no random steps.
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